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

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

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

Multiply the exponents in <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></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> .

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

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

Multiply the exponents in <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mn>3</mn><mi>d</mi></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> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Divide each term in <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mo>-</mo><mn>2</mn><mo>+</mo><mn>6</mn><mi>d</mi></mrow></msup><mo>=</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Simplify the left side.

Simplify the denominator.

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

One to any power is one.

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

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mo>-</mo><mn>2</mn><mo>+</mo><mn>6</mn><mi>d</mi></mrow></msup><mo>⋅</mo><mn>4</mn></mstyle></math> .

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

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>6</mn><mi>d</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Simplify the right side.

Simplify the denominator.

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

One to any power is one.

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

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Create equivalent expressions in the equation that all have equal bases.

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

Divide each term in <math><mstyle displaystyle="true"><mn>6</mn><mi>d</mi><mo>=</mo><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Cancel the common factor.

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

Simplify the right side.

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

Cancel the common factors.

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

Cancel the common factor.

Rewrite the expression.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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