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

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

Step 1

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

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

Step 2

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

Move $b^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Step 3

Cancel the common factor of $a^{3}$ and $a$ .

Factor $a$ out of $a^{3}$ .

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

Cancel the common factors.

Factor $a$ out of $a b^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{a^{2}}{b^{3}}$