Simplify (a^2b^-3)(ab^2)

$(a^{2} b^{- 3}) (a b^{2})$

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

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Move $a$ .

$a \cdot a^{2} b^{- 3} b^{2}$

Multiply $a$ by $a^{2}$ .

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Raise $a$ to the power of $1$ .

$a^{1} a^{2} b^{- 3} b^{2}$

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

$a^{1 + 2} b^{- 3} b^{2}$

Add $1$ and $2$ .

$a^{3} b^{- 3} b^{2}$

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

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Move $b^{2}$ .

$a^{3} (b^{2} b^{- 3})$

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

$a^{3} b^{2 - 3}$

Subtract $3$ from $2$ .

$a^{3} b^{- 1}$

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

$a^{3} \frac{1}{b}$

Combine $a^{3}$ and $\frac{1}{b}$ .

$\frac{a^{3}}{b}$

Simplify (a^2b^-3)(ab^2)

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