Write with Rational (Fractional) Exponents ( cube root of 9)^2

${(\sqrt[3]{9})}^{2}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{9}$ as $9^{\frac{1}{3}}$ .

${(9^{\frac{1}{3}})}^{2}$

Multiply the exponents in ${(9^{\frac{1}{3}})}^{2}$ .

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

$9^{\frac{1}{3} \cdot 2}$

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

$9^{\frac{2}{3}}$