Simplify ((2x)/3)^-3

${(\frac{2 x}{3})}^{- 3}$

Step 1

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

${(\frac{3}{2 x})}^{3}$

Step 2

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

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

$\frac{3^{3}}{{(2 x)}^{3}}$

Apply the product rule to $2 x$ .

$\frac{3^{3}}{2^{3} x^{3}}$

Step 3

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

$\frac{27}{2^{3} x^{3}}$

Step 4

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

$\frac{27}{8 x^{3}}$