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

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

Step 1

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

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

Step 2

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

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

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

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

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

Step 3

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

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

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

Multiply $3$ by $3$ .

$\frac{y^{9}}{2^{3} {(x^{2})}^{3}}$

Step 4

Simplify the denominator.

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

$\frac{y^{9}}{8 {(x^{2})}^{3}}$

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

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

$\frac{y^{9}}{8 x^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{y^{9}}{8 x^{6}}$