Write with Rational (Fractional) Exponents ( cube root of 5)^4

${(\sqrt[3]{5})}^{4}$

Step 1

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

${(5^{\frac{1}{3}})}^{4}$

Step 2

Multiply the exponents in ${(5^{\frac{1}{3}})}^{4}$ .

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

$5^{\frac{1}{3} \cdot 4}$

Combine $\frac{1}{3}$ and $4$ .

$5^{\frac{4}{3}}$