Write with Rational (Fractional) Exponents ( cube root of a)^2

${(\sqrt[3]{a})}^{2}$

Step 1

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

${(a^{\frac{1}{3}})}^{2}$

Step 2

Multiply the exponents in ${(a^{\frac{1}{3}})}^{2}$ .

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

$a^{\frac{1}{3} \cdot 2}$

Combine $\frac{1}{3}$ and $2$ .

$a^{\frac{2}{3}}$