Simplify (5^4)^(1/2)

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

Step 1

Multiply the exponents in ${(5^{4})}^{\frac{1}{2}}$ .

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$5^{2 (2) \frac{1}{2}}$

Cancel the common factor.

$5^{2 \cdot 2 \frac{1}{2}}$

Rewrite the expression.

$5^{2}$

Step 2

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

$25$