Simplify (3a^9r^-3)/(-4(a^2)^-1)

$\frac{3 a^{9} r^{- 3}}{- 4 {(a^{2})}^{- 1}}$

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

$\frac{3 a^{9}}{- 4 {(a^{2})}^{- 1} r^{3}}$

Move ${(a^{2})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3 a^{9} a^{2}}{- 4 r^{3}}$

Multiply $a^{9}$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$\frac{3 (a^{2} a^{9})}{- 4 r^{3}}$

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

$\frac{3 a^{2 + 9}}{- 4 r^{3}}$

Add $2$ and $9$ .

$\frac{3 a^{11}}{- 4 r^{3}}$

Move the negative in front of the fraction.

$- \frac{3 a^{11}}{4 r^{3}}$