Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mn>60</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

The exact value of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mn>60</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Apply the distributive property.

Combine <math><mstyle displaystyle="true"><msqrt><mn>14</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><msqrt><mn>14</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mi>i</mi><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine using the product rule for radicals.

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>14</mn></mstyle></math> .

Use the Binomial Theorem.

Simplify each term.

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>a</mi><mi>b</mi><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mi>n</mi></mrow></msup></mstyle></math> to distribute the exponent.

Apply the product rule to <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>4</mn></mrow></msup></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mn>4</mn></mrow></msup></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the numerator.

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>14</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mn>14</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>14</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>14</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>196</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>196</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn><msup><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>a</mi><mi>b</mi><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mi>n</mi></mrow></msup></mstyle></math> to distribute the exponent.

Apply the product rule to <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Simplify the numerator.

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mn>14</mn></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>14</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>2744</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>14</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>14</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>196</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2744</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>196</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>14</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>14</mn><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>8</mn></mrow></mfrac></mstyle></math> into the numerator.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><mo>-</mo><mn>14</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>14</mn><msqrt><mn>14</mn></msqrt></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>7</mn><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mrow><mo>(</mo><msqrt><mn>42</mn></msqrt><mi>i</mi><mo>)</mo></mrow></mstyle></math> .

Combine <math><mstyle displaystyle="true"><msqrt><mn>42</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>7</mn><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine using the product rule for radicals.

Multiply <math><mstyle displaystyle="true"><mn>42</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>14</mn></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>7</mn><msqrt><mn>588</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Simplify the numerator.

Rewrite <math><mstyle displaystyle="true"><mn>588</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>14</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>3</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>196</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>588</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>196</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>14</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Multiply <math><mstyle displaystyle="true"><mn>14</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>98</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mi>i</mi><mo>⋅</mo><mn>98</mn><msqrt><mn>3</mn></msqrt></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mi>i</mi><mo>⋅</mo><mn>49</mn><msqrt><mn>3</mn></msqrt></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>49</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>49</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>a</mi><mi>b</mi><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mi>n</mi></mrow></msup></mstyle></math> to distribute the exponent.

Apply the product rule to <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>14</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mn>14</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>14</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Evaluate the exponent.

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>14</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>14</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>42</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>42</mn></msqrt><mi>i</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><msqrt><mn>42</mn></msqrt><mi>i</mi></mstyle></math> .

Simplify the numerator.

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>42</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>42</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mn>42</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>42</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Evaluate the exponent.

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>42</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mo>-</mo><mn>42</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>42</mn></mstyle></math> .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Multiply <math><mstyle displaystyle="true"><mn>21</mn><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>21</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>21</mn></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mo>-</mo><mn>21</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>21</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>21</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>21</mn></mstyle></math> .

Move the negative in front of the fraction.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> into the numerator.

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>42</mn></msqrt><mi>i</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><msqrt><mn>42</mn></msqrt><mi>i</mi></mstyle></math> .

Simplify the numerator.

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>42</mn></msqrt></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mn>42</mn></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>42</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>74088</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>42</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>42</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>1764</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>74088</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>1764</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>42</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Factor out <math><mstyle displaystyle="true"><msup><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mi>i</mi></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mi>i</mi></mstyle></math> .

Combine exponents.

Factor out negative.

Multiply <math><mstyle displaystyle="true"><mn>42</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn><msqrt><mn>14</mn></msqrt></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>42</mn><msqrt><mn>42</mn></msqrt><mi>i</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><msqrt><mn>14</mn></msqrt></mstyle></math> .

Combine using the product rule for radicals.

Multiply <math><mstyle displaystyle="true"><mn>14</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>42</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mo>-</mo><mn>42</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>42</mn><msqrt><mn>588</mn></msqrt><mi>i</mi></mstyle></math> .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Simplify the numerator.

Rewrite <math><mstyle displaystyle="true"><mn>588</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>14</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>3</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>196</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>588</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>196</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>14</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>21</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>14</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mo>-</mo><mn>294</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>294</mn><msqrt><mn>3</mn></msqrt><mi>i</mi></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mo>-</mo><mn>147</mn><msqrt><mn>3</mn></msqrt><mi>i</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>147</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>42</mn></msqrt><mi>i</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><msqrt><mn>42</mn></msqrt><mi>i</mi></mstyle></math> .

Simplify the numerator.

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>42</mn></msqrt></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>42</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mn>42</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>42</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>42</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mi>i</mi></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mi>i</mi></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>1764</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>1764</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>1764</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Simplify terms.

Combine fractions with similar denominators.

Add <math><mstyle displaystyle="true"><mn>49</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>441</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>490</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>490</mn></mstyle></math> .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Combine fractions with similar denominators.

Simplify the expression.

Subtract <math><mstyle displaystyle="true"><mn>441</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>245</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mo>-</mo><mn>196</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Reorder the factors of <math><mstyle displaystyle="true"><mn>147</mn><msqrt><mn>3</mn></msqrt><mi>i</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>49</mn><mi>i</mi><msqrt><mn>3</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><mn>147</mn><mi>i</mi><msqrt><mn>3</mn></msqrt></mstyle></math> .

Reorder <math><mstyle displaystyle="true"><mn>98</mn><mi>i</mi><msqrt><mn>3</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><mo>-</mo><mn>98</mn></mstyle></math> .

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Name | two billion forty-eight million seven thousand one hundred seventy |
---|

- 2048007170 has 64 divisors, whose sum is
**4270516992** - The reverse of 2048007170 is
**0717008402** - Previous prime number is
**391**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 29
- Digital Root 2

Name | one billion four hundred twenty-six million four hundred thirty-nine thousand four hundred thirty-five |
---|

- 1426439435 has 4 divisors, whose sum is
**1711727328** - The reverse of 1426439435 is
**5349346241** - Previous prime number is
**5**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 41
- Digital Root 5

Name | twenty million six hundred forty thousand six hundred seventy-five |
---|

- 20640675 has 32 divisors, whose sum is
**31629312** - The reverse of 20640675 is
**57604602** - Previous prime number is
**127**

- Is Prime? no
- Number parity odd
- Number length 8
- Sum of Digits 30
- Digital Root 3