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Evaluate (((-5)^3)^2)÷((-5)^2)

${({(- 5)}^{3})}^{2} \div {(- 5)}^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{{({(- 5)}^{3})}^{2}}{{(- 5)}^{2}}$

Step 2

Simplify the numerator.

Multiply the exponents in ${({(- 5)}^{3})}^{2}$ .

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

$\frac{{(- 5)}^{3 \cdot 2}}{{(- 5)}^{2}}$

Multiply $3$ by $2$ .

$\frac{{(- 5)}^{6}}{{(- 5)}^{2}}$

$\frac{{(- 5)}^{6}}{{(- 5)}^{2}}$

Raise $- 5$ to the power of $6$ .

$\frac{15625}{{(- 5)}^{2}}$

$\frac{15625}{{(- 5)}^{2}}$

Step 3

Simplify the expression.

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

$\frac{15625}{25}$

Divide $15625$ by $25$ .

$625$

$625$

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