Write with Rational (Fractional) Exponents ( fifth root of 8)^4

${(\sqrt[5]{8})}^{4}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{8}$ as $8^{\frac{1}{5}}$ .

${(8^{\frac{1}{5}})}^{4}$

Step 2

Multiply the exponents in ${(8^{\frac{1}{5}})}^{4}$ .

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

$8^{\frac{1}{5} \cdot 4}$

Combine $\frac{1}{5}$ and $4$ .

$8^{\frac{4}{5}}$