Trigonometry Examples

$v ({(- \frac{24}{25})}^{2} + {(- \frac{7}{25})}^{2})$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the product rule to $- \frac{24}{25}$ .

$v ({(- 1)}^{2} {(\frac{24}{25})}^{2} + {(- \frac{7}{25})}^{2})$

Step 1.1.2

Apply the product rule to $\frac{24}{25}$ .

$v ({(- 1)}^{2} \frac{24^{2}}{25^{2}} + {(- \frac{7}{25})}^{2})$

Step 1.2

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

$v (1 \frac{24^{2}}{25^{2}} + {(- \frac{7}{25})}^{2})$

Step 1.3

Multiply $\frac{24^{2}}{25^{2}}$ by $1$ .

$v (\frac{24^{2}}{25^{2}} + {(- \frac{7}{25})}^{2})$

Step 1.4

Raise $24$ to the power of $2$ .

$v (\frac{576}{25^{2}} + {(- \frac{7}{25})}^{2})$

Step 1.5

Raise $25$ to the power of $2$ .

$v (\frac{576}{625} + {(- \frac{7}{25})}^{2})$

Step 1.6

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

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Step 1.6.1

Apply the product rule to $- \frac{7}{25}$ .

$v (\frac{576}{625} + {(- 1)}^{2} {(\frac{7}{25})}^{2})$

Step 1.6.2

Apply the product rule to $\frac{7}{25}$ .

$v (\frac{576}{625} + {(- 1)}^{2} \frac{7^{2}}{25^{2}})$

Step 1.7

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

$v (\frac{576}{625} + 1 \frac{7^{2}}{25^{2}})$

Step 1.8

Multiply $\frac{7^{2}}{25^{2}}$ by $1$ .

$v (\frac{576}{625} + \frac{7^{2}}{25^{2}})$

Step 1.9

Raise $7$ to the power of $2$ .

$v (\frac{576}{625} + \frac{49}{25^{2}})$

Step 1.10

Raise $25$ to the power of $2$ .

$v (\frac{576}{625} + \frac{49}{625})$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$v \frac{576 + 49}{625}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Add $576$ and $49$ .

$v \frac{625}{625}$

Step 2.2.2

Divide $625$ by $625$ .

$v \cdot 1$

Step 2.2.3

Multiply $v$ by $1$ .

$v$