Write in Exponential Form -( fourth root of 6m^2)^3

$- {(\sqrt[4]{6 m^{2}})}^{3}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{6 m^{2}}$ as ${(6 m^{2})}^{\frac{1}{4}}$ .

$- {({(6 m^{2})}^{\frac{1}{4}})}^{3}$

Multiply the exponents in ${({(6 m^{2})}^{\frac{1}{4}})}^{3}$ .

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

$- {(6 m^{2})}^{\frac{1}{4} \cdot 3}$

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

$- {(6 m^{2})}^{\frac{3}{4}}$