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

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

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{4}}$ as $x^{\frac{4}{3}}$ .

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

Step 2

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

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

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

Multiply $\frac{4}{3} \cdot 5$ .

Combine $\frac{4}{3}$ and $5$ .

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

Multiply $4$ by $5$ .

$x^{\frac{20}{3}}$