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

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

Step 1

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

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

Step 2

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

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

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

Apply the product rule to $x^{2} y$ .

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

Step 3

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

$\frac{8}{{(x^{2})}^{3} y^{3}}$

Step 4

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

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

$\frac{8}{x^{2 \cdot 3} y^{3}}$

Multiply $2$ by $3$ .

$\frac{8}{x^{6} y^{3}}$