Write in Exponential Form ( cube root of 3a)^4

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

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

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

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

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

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

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

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