Simplify (25^(1/2))^3

${(25^{\frac{1}{2}})}^{3}$

Step 1

Simplify the expression.

Multiply the exponents in ${(25^{\frac{1}{2}})}^{3}$ .

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

$25^{\frac{1}{2} \cdot 3}$

Combine $\frac{1}{2}$ and $3$ .

$25^{\frac{3}{2}}$

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

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

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

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

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$5^{3}$

Step 3

Raise $5$ to the power of $3$ .

$125$