Simplify ((a^2b)/(a^-3b^2))^-1

${(\frac{a^{2} b}{a^{- 3} b^{2}})}^{- 1}$

Step 1

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

${(\frac{a^{2} b a^{3}}{b^{2}})}^{- 1}$

Step 2

Multiply $a^{2}$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

${(\frac{a^{3} a^{2} b}{b^{2}})}^{- 1}$

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

${(\frac{a^{3 + 2} b}{b^{2}})}^{- 1}$

Add $3$ and $2$ .

${(\frac{a^{5} b}{b^{2}})}^{- 1}$

Step 3

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

Factor $b$ out of $a^{5} b$ .

${(\frac{b a^{5}}{b^{2}})}^{- 1}$

Cancel the common factors.

Factor $b$ out of $b^{2}$ .

${(\frac{b a^{5}}{b \cdot b})}^{- 1}$

Cancel the common factor.

${(\frac{b a^{5}}{b \cdot b})}^{- 1}$

Rewrite the expression.

${(\frac{a^{5}}{b})}^{- 1}$

Step 4

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

$\frac{b}{a^{5}}$