Simplify (p3/2)^-2

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

Combine $p$ and $\frac{3}{2}$ .

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

Move $3$ to the left of $p$ .

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

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

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

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

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

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

Apply the product rule to $3 p$ .

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

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

$\frac{4}{3^{2} p^{2}}$

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

$\frac{4}{9 p^{2}}$