Evaluate ((-5)^6*25^2)/125

$\frac{{(- 5)}^{6} \cdot 25^{2}}{125}$

Step 1

Simplify the numerator.

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{{(- 1 (5))}^{6} \cdot 25^{2}}{125}$

Apply the product rule to $- 1 (5)$ .

$\frac{{(- 1)}^{6} \cdot 5^{6} \cdot 25^{2}}{125}$

Raise $- 1$ to the power of $6$ .

$\frac{1 \cdot 5^{6} \cdot 25^{2}}{125}$

Multiply $5^{6}$ by $1$ .

$\frac{5^{6} \cdot 25^{2}}{125}$

Rewrite $25$ as $5^{2}$ .

$\frac{5^{6} \cdot {(5^{2})}^{2}}{125}$

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

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

$\frac{5^{6} \cdot 5^{2 \cdot 2}}{125}$

Multiply $2$ by $2$ .

$\frac{5^{6} \cdot 5^{4}}{125}$

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

$\frac{5^{6 + 4}}{125}$

Add $6$ and $4$ .

$\frac{5^{10}}{125}$

Step 2

Simplify the expression.

Raise $5$ to the power of $10$ .

$\frac{9765625}{125}$

Divide $9765625$ by $125$ .

$78125$