Write in Exponential Form ( cube root of 9ab)^4

${(\sqrt[3]{9 a b})}^{4}$

Step 1

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

${({(9 a b)}^{\frac{1}{3}})}^{4}$

Step 2

Multiply the exponents in ${({(9 a b)}^{\frac{1}{3}})}^{4}$ .

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

${(9 a b)}^{\frac{1}{3} \cdot 4}$

Combine $\frac{1}{3}$ and $4$ .

${(9 a b)}^{\frac{4}{3}}$