Evaluate (625^2)^(1/8)

${(625^{2})}^{\frac{1}{8}}$

Step 1

Simplify the expression.

Multiply the exponents in ${(625^{2})}^{\frac{1}{8}}$ .

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

$625^{2 (\frac{1}{8})}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$625^{2 \frac{1}{2 (4)}}$

Cancel the common factor.

$625^{2 \frac{1}{2 \cdot 4}}$

Rewrite the expression.

$625^{\frac{1}{4}}$

Rewrite $625$ as $5^{4}$ .

${(5^{4})}^{\frac{1}{4}}$

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

$5^{4 (\frac{1}{4})}$

Step 2

Cancel the common factor of $4$ .

Cancel the common factor.

$5^{4 (\frac{1}{4})}$

Rewrite the expression.

$5^{1}$

Step 3

Evaluate the exponent.

$5$