Simplify (6m^2n^-1)^3

${(6 m^{2} n^{- 1})}^{3}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Multiply $6 m^{2} \frac{1}{n}$ .

Combine $6$ and $\frac{1}{n}$ .

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

Combine $m^{2}$ and $\frac{6}{n}$ .

${(\frac{m^{2} \cdot 6}{n})}^{3}$

Move $6$ to the left of $m^{2}$ .

${(\frac{6 \cdot m^{2}}{n})}^{3}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

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

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

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

Simplify the numerator.

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

$\frac{216 {(m^{2})}^{3}}{n^{3}}$

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

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

$\frac{216 m^{2 \cdot 3}}{n^{3}}$

Multiply $2$ by $3$ .

$\frac{216 m^{6}}{n^{3}}$