Simplify ((p^2)/(q^3))(p/q)^-2

$(\frac{p^{2}}{q^{3}}) {(\frac{p}{q})}^{- 2}$

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

$\frac{p^{2}}{q^{3}} {(\frac{q}{p})}^{2}$

Apply the product rule to $\frac{q}{p}$ .

$\frac{p^{2}}{q^{3}} \cdot \frac{q^{2}}{p^{2}}$

Combine.

$\frac{p^{2} q^{2}}{q^{3} p^{2}}$

Cancel the common factor of $p^{2}$ .

Cancel the common factor.

$\frac{p^{2} q^{2}}{q^{3} p^{2}}$

Rewrite the expression.

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

Cancel the common factor of $q^{2}$ and $q^{3}$ .

Multiply by $1$ .

$\frac{q^{2} \cdot 1}{q^{3}}$

Cancel the common factors.

Factor $q^{2}$ out of $q^{3}$ .

$\frac{q^{2} \cdot 1}{q^{2} q}$

Cancel the common factor.

$\frac{q^{2} \cdot 1}{q^{2} q}$

Rewrite the expression.

$\frac{1}{q}$