Write in Exponential Form ( cube root of 5)^3

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

Step 1

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

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

Step 2

Multiply the exponents in ${(5^{\frac{1}{3}})}^{3}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$5^{1}$

Step 3

Evaluate the exponent.

$5$