Simplify the Radical Expression ( cube root of 25)^3

${(\sqrt[3]{25})}^{3}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{25}$ as $25^{\frac{1}{3}}$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$25^{1}$

Step 5

Evaluate the exponent.

$25$