Simplify the Radical Expression ( cube root of 5)^3

${(\sqrt[3]{5})}^{3}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5}$ as $5^{\frac{1}{3}}$ .

${(5^{\frac{1}{3}})}^{3}$

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

$5^{\frac{1}{3} \cdot 3}$

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

$5^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$5^{\frac{3}{3}}$

Rewrite the expression.

$5^{1}$

Evaluate the exponent.

$5$