Simplify ((2m)/(3n))^-3

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

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 2

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

Apply the product rule to $\frac{3 n}{2 m}$ .

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

Apply the product rule to $3 n$ .

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

Apply the product rule to $2 m$ .

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

Step 3

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

$\frac{27 n^{3}}{2^{3} m^{3}}$

Step 4

Raise $2$ to the power of $3$ .

$\frac{27 n^{3}}{8 m^{3}}$