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

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

Step 1

Multiply the exponents in ${(p^{\frac{3}{2}})}^{- 2}$ .

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$p^{\frac{3}{2} \cdot (2 (- 1))}$

Cancel the common factor.

$p^{\frac{3}{2} \cdot (2 \cdot - 1)}$

Rewrite the expression.

$p^{3 \cdot - 1}$

Multiply $3$ by $- 1$ .

$p^{- 3}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{p^{3}}$