Evaluate (-2/( square root of 29))^2-(-5/( square root of 29))^2

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Trigonometry

${(- \frac{2}{\sqrt{29}})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Simplify each term.

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Multiply $\frac{2}{\sqrt{29}}$ by $\frac{\sqrt{29}}{\sqrt{29}}$ .

${(- (\frac{2}{\sqrt{29}} \cdot \frac{\sqrt{29}}{\sqrt{29}}))}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Combine and simplify the denominator.

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Multiply $\frac{2}{\sqrt{29}}$ and $\frac{\sqrt{29}}{\sqrt{29}}$ .

${(- \frac{2 \sqrt{29}}{\sqrt{29} \sqrt{29}})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Raise $\sqrt{29}$ to the power of $1$ .

${(- \frac{2 \sqrt{29}}{{\sqrt{29}}^{1} \sqrt{29}})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Raise $\sqrt{29}$ to the power of $1$ .

${(- \frac{2 \sqrt{29}}{{\sqrt{29}}^{1} {\sqrt{29}}^{1}})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(- \frac{2 \sqrt{29}}{{\sqrt{29}}^{1 + 1}})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Add $1$ and $1$ .

${(- \frac{2 \sqrt{29}}{{\sqrt{29}}^{2}})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Rewrite ${\sqrt{29}}^{2}$ as $29$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{29}$ as $29^{\frac{1}{2}}$ .

${(- \frac{2 \sqrt{29}}{{(29^{\frac{1}{2}})}^{2}})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(- \frac{2 \sqrt{29}}{29^{\frac{1}{2} \cdot 2}})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Combine $\frac{1}{2}$ and $2$ .

${(- \frac{2 \sqrt{29}}{29^{\frac{2}{2}}})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

${(- \frac{2 \sqrt{29}}{29^{\frac{2}{2}}})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Divide $1$ by $1$ .

${(- \frac{2 \sqrt{29}}{29^{1}})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Evaluate the exponent.

${(- \frac{2 \sqrt{29}}{29})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Apply the product rule to $- \frac{2 \sqrt{29}}{29}$ .

${(- 1)}^{2} {(\frac{2 \sqrt{29}}{29})}^{2} - {(- \frac{5}{\sqrt{29}})}^{2}$

Apply the product rule to $\frac{2 \sqrt{29}}{29}$ .

${(- 1)}^{2} \frac{{(2 \sqrt{29})}^{2}}{29^{2}} - {(- \frac{5}{\sqrt{29}})}^{2}$

Apply the product rule to $2 \sqrt{29}$ .

${(- 1)}^{2} \frac{2^{2} {\sqrt{29}}^{2}}{29^{2}} - {(- \frac{5}{\sqrt{29}})}^{2}$

Raise $- 1$ to the power of $2$ .

$1 \frac{2^{2} {\sqrt{29}}^{2}}{29^{2}} - {(- \frac{5}{\sqrt{29}})}^{2}$

Multiply $\frac{2^{2} {\sqrt{29}}^{2}}{29^{2}}$ by $1$ .

$\frac{2^{2} {\sqrt{29}}^{2}}{29^{2}} - {(- \frac{5}{\sqrt{29}})}^{2}$

Simplify the numerator.

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Raise $2$ to the power of $2$ .

$\frac{4 {\sqrt{29}}^{2}}{29^{2}} - {(- \frac{5}{\sqrt{29}})}^{2}$

Rewrite ${\sqrt{29}}^{2}$ as $29$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{29}$ as $29^{\frac{1}{2}}$ .

$\frac{4 {(29^{\frac{1}{2}})}^{2}}{29^{2}} - {(- \frac{5}{\sqrt{29}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4 \cdot 29^{\frac{1}{2} \cdot 2}}{29^{2}} - {(- \frac{5}{\sqrt{29}})}^{2}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{4 \cdot 29^{\frac{2}{2}}}{29^{2}} - {(- \frac{5}{\sqrt{29}})}^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{4 \cdot 29^{\frac{2}{2}}}{29^{2}} - {(- \frac{5}{\sqrt{29}})}^{2}$

Divide $1$ by $1$ .

$\frac{4 \cdot 29^{1}}{29^{2}} - {(- \frac{5}{\sqrt{29}})}^{2}$

Evaluate the exponent.

$\frac{4 \cdot 29}{29^{2}} - {(- \frac{5}{\sqrt{29}})}^{2}$

Raise $29$ to the power of $2$ .

$\frac{4 \cdot 29}{841} - {(- \frac{5}{\sqrt{29}})}^{2}$

Multiply $4$ by $29$ .

$\frac{116}{841} - {(- \frac{5}{\sqrt{29}})}^{2}$

Cancel the common factor of $116$ and $841$ .

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Factor $29$ out of $116$ .

$\frac{29 (4)}{841} - {(- \frac{5}{\sqrt{29}})}^{2}$

Cancel the common factors.

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Factor $29$ out of $841$ .

$\frac{29 \cdot 4}{29 \cdot 29} - {(- \frac{5}{\sqrt{29}})}^{2}$

Cancel the common factor.

$\frac{29 \cdot 4}{29 \cdot 29} - {(- \frac{5}{\sqrt{29}})}^{2}$

Rewrite the expression.

$\frac{4}{29} - {(- \frac{5}{\sqrt{29}})}^{2}$

Multiply $\frac{5}{\sqrt{29}}$ by $\frac{\sqrt{29}}{\sqrt{29}}$ .

$\frac{4}{29} - {(- (\frac{5}{\sqrt{29}} \cdot \frac{\sqrt{29}}{\sqrt{29}}))}^{2}$

Combine and simplify the denominator.

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Multiply $\frac{5}{\sqrt{29}}$ and $\frac{\sqrt{29}}{\sqrt{29}}$ .

$\frac{4}{29} - {(- \frac{5 \sqrt{29}}{\sqrt{29} \sqrt{29}})}^{2}$

Raise $\sqrt{29}$ to the power of $1$ .

$\frac{4}{29} - {(- \frac{5 \sqrt{29}}{{\sqrt{29}}^{1} \sqrt{29}})}^{2}$

Raise $\sqrt{29}$ to the power of $1$ .

$\frac{4}{29} - {(- \frac{5 \sqrt{29}}{{\sqrt{29}}^{1} {\sqrt{29}}^{1}})}^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4}{29} - {(- \frac{5 \sqrt{29}}{{\sqrt{29}}^{1 + 1}})}^{2}$

Add $1$ and $1$ .

$\frac{4}{29} - {(- \frac{5 \sqrt{29}}{{\sqrt{29}}^{2}})}^{2}$

Rewrite ${\sqrt{29}}^{2}$ as $29$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{29}$ as $29^{\frac{1}{2}}$ .

$\frac{4}{29} - {(- \frac{5 \sqrt{29}}{{(29^{\frac{1}{2}})}^{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4}{29} - {(- \frac{5 \sqrt{29}}{29^{\frac{1}{2} \cdot 2}})}^{2}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{4}{29} - {(- \frac{5 \sqrt{29}}{29^{\frac{2}{2}}})}^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{4}{29} - {(- \frac{5 \sqrt{29}}{29^{\frac{2}{2}}})}^{2}$

Divide $1$ by $1$ .

$\frac{4}{29} - {(- \frac{5 \sqrt{29}}{29^{1}})}^{2}$

Evaluate the exponent.

$\frac{4}{29} - {(- \frac{5 \sqrt{29}}{29})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Apply the product rule to $- \frac{5 \sqrt{29}}{29}$ .

$\frac{4}{29} - ({(- 1)}^{2} {(\frac{5 \sqrt{29}}{29})}^{2})$

Apply the product rule to $\frac{5 \sqrt{29}}{29}$ .

$\frac{4}{29} - ({(- 1)}^{2} \frac{{(5 \sqrt{29})}^{2}}{29^{2}})$

Apply the product rule to $5 \sqrt{29}$ .

$\frac{4}{29} - ({(- 1)}^{2} \frac{5^{2} {\sqrt{29}}^{2}}{29^{2}})$

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

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Move ${(- 1)}^{2}$ .

$\frac{4}{29} + {(- 1)}^{2} \cdot - 1 \frac{5^{2} {\sqrt{29}}^{2}}{29^{2}}$

Multiply ${(- 1)}^{2}$ by $- 1$ .

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Raise $- 1$ to the power of $1$ .

$\frac{4}{29} + {(- 1)}^{2} \cdot {(- 1)}^{1} \frac{5^{2} {\sqrt{29}}^{2}}{29^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4}{29} + {(- 1)}^{2 + 1} \frac{5^{2} {\sqrt{29}}^{2}}{29^{2}}$

Add $2$ and $1$ .

$\frac{4}{29} + {(- 1)}^{3} \frac{5^{2} {\sqrt{29}}^{2}}{29^{2}}$

Raise $- 1$ to the power of $3$ .

$\frac{4}{29} - \frac{5^{2} {\sqrt{29}}^{2}}{29^{2}}$

Simplify the numerator.

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Raise $5$ to the power of $2$ .

$\frac{4}{29} - \frac{25 {\sqrt{29}}^{2}}{29^{2}}$

Rewrite ${\sqrt{29}}^{2}$ as $29$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{29}$ as $29^{\frac{1}{2}}$ .

$\frac{4}{29} - \frac{25 {(29^{\frac{1}{2}})}^{2}}{29^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4}{29} - \frac{25 \cdot 29^{\frac{1}{2} \cdot 2}}{29^{2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{4}{29} - \frac{25 \cdot 29^{\frac{2}{2}}}{29^{2}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{4}{29} - \frac{25 \cdot 29^{\frac{2}{2}}}{29^{2}}$

Divide $1$ by $1$ .

$\frac{4}{29} - \frac{25 \cdot 29^{1}}{29^{2}}$

Evaluate the exponent.

$\frac{4}{29} - \frac{25 \cdot 29}{29^{2}}$

Raise $29$ to the power of $2$ .

$\frac{4}{29} - \frac{25 \cdot 29}{841}$

Multiply $25$ by $29$ .

$\frac{4}{29} - \frac{725}{841}$

Cancel the common factor of $725$ and $841$ .

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Factor $29$ out of $725$ .

$\frac{4}{29} - \frac{29 (25)}{841}$

Cancel the common factors.

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Factor $29$ out of $841$ .

$\frac{4}{29} - \frac{29 \cdot 25}{29 \cdot 29}$

Cancel the common factor.

$\frac{4}{29} - \frac{29 \cdot 25}{29 \cdot 29}$

Rewrite the expression.

$\frac{4}{29} - \frac{25}{29}$

Combine the numerators over the common denominator.

$\frac{4 - 25}{29}$

Subtract $25$ from $4$ .

$\frac{- 21}{29}$

Move the negative in front of the fraction.

$- \frac{21}{29}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{21}{29}$

Decimal Form:

$- 0.72413793 \dots$

Do you know how to Evaluate (-2/( square root of 29))^2-(-5/( square root of 29))^2? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name

Name	one billion six hundred ninety-four million six hundred one thousand nine hundred ninety-seven

Interesting facts

1694601997 has 8 divisors, whose sum is 1850679360
The reverse of 1694601997 is 7991064961
Previous prime number is 919

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 52
Digital Root 7

Name

Name	one billion three hundred forty-three million three hundred ninety thousand five hundred ninety-four

Interesting facts

1343390594 has 8 divisors, whose sum is 2037229968
The reverse of 1343390594 is 4950933431
Previous prime number is 91

Basic properties

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

Name

Name	two hundred seventy-two million six hundred thirty thousand fifty-nine

Interesting facts

272630059 has 8 divisors, whose sum is 293730192
The reverse of 272630059 is 950036272
Previous prime number is 4253

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 34
Digital Root 7

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