Simplify -( fourth root of 6m^2)^3

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

Step 1

Rewrite ${\sqrt[4]{6 m^{2}}}^{3}$ as ${({(6 m^{2})}^{3})}^{\frac{1}{4}}$ .

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

Step 2

Apply the product rule to $6 m^{2}$ .

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

Step 3

Raise $6$ to the power of $3$ .

$- \sqrt[4]{216 {(m^{2})}^{3}}$

Step 4

Multiply the exponents in ${(m^{2})}^{3}$ .

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

$- \sqrt[4]{216 m^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$- \sqrt[4]{216 m^{6}}$

Step 5

Rewrite $216 m^{6}$ as $m^{4} \cdot (216 m^{2})$ .

Factor out $m^{4}$ .

$- \sqrt[4]{216 (m^{4} m^{2})}$

Reorder $216$ and $m^{4}$ .

$- \sqrt[4]{m^{4} \cdot 216 m^{2}}$

Add parentheses.

$- \sqrt[4]{m^{4} \cdot (216 m^{2})}$

Step 6

Pull terms out from under the radical.

$- m \sqrt[4]{216 m^{2}}$