Write with Rational (Fractional) Exponents ( cube root of 7)^5

${(\sqrt[3]{7})}^{5}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{7}$ as $7^{\frac{1}{3}}$ .

${(7^{\frac{1}{3}})}^{5}$

Step 2

Multiply the exponents in ${(7^{\frac{1}{3}})}^{5}$ .

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

$7^{\frac{1}{3} \cdot 5}$

Combine $\frac{1}{3}$ and $5$ .

$7^{\frac{5}{3}}$