Divide (a^4b^-3)/(ab^-2)

$\frac{a^{4} b^{- 3}}{a b^{- 2}}$

Step 1

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

$\frac{a^{4}}{a b^{- 2} b^{3}}$

Step 2

Simplify the denominator.

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

Move $b^{3}$ .

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

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

$\frac{a^{4}}{a b^{3 - 2}}$

Subtract $2$ from $3$ .

$\frac{a^{4}}{a b^{1}}$

Simplify $a b^{1}$ .

$\frac{a^{4}}{a b}$

Step 3

Cancel the common factor of $a^{4}$ and $a$ .

Factor $a$ out of $a^{4}$ .

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

Cancel the common factors.

Factor $a$ out of $a b$ .

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

Cancel the common factor.

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

Rewrite the expression.

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