Write in Exponential Form ( square root of 2ab)^3

${(\sqrt{2 a b})}^{3}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 a b}$ as ${(2 a b)}^{\frac{1}{2}}$ .

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

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

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

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

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

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