Simplify (3q^2)/(-2(p^3q^-5)^-1)

$\frac{3 q^{2}}{- 2 {(p^{3} q^{- 5})}^{- 1}}$

Move ${(p^{3} q^{- 5})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3 q^{2} (p^{3} q^{- 5})}{- 2}$

Multiply $q^{2}$ by $q^{- 5}$ by adding the exponents.

Move $q^{- 5}$ .

$\frac{3 (q^{- 5} q^{2}) p^{3}}{- 2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 q^{- 5 + 2} p^{3}}{- 2}$

Add $- 5$ and $2$ .

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

Move $q^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Move the negative in front of the fraction.

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