Divide (p^-4q^5r^6)/(p^-3qr^-2)

$\frac{p^{- 4} q^{5} r^{6}}{p^{- 3} q r^{- 2}}$

Step 1

Move $p^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{q^{5} r^{6}}{p^{- 3} q r^{- 2} p^{4}}$

Step 2

Simplify the denominator.

Multiply $p^{- 3}$ by $p^{4}$ by adding the exponents.

Move $p^{4}$ .

$\frac{q^{5} r^{6}}{p^{4} p^{- 3} q r^{- 2}}$

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

$\frac{q^{5} r^{6}}{p^{4 - 3} q r^{- 2}}$

Subtract $3$ from $4$ .

$\frac{q^{5} r^{6}}{p^{1} q r^{- 2}}$

Simplify $p^{1} q r^{- 2}$ .

$\frac{q^{5} r^{6}}{p q r^{- 2}}$

Step 3

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

$\frac{q^{5} r^{6} r^{2}}{p q}$

Step 4

Multiply $r^{6}$ by $r^{2}$ by adding the exponents.

Move $r^{2}$ .

$\frac{q^{5} (r^{2} r^{6})}{p q}$

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

$\frac{q^{5} r^{2 + 6}}{p q}$

Add $2$ and $6$ .

$\frac{q^{5} r^{8}}{p q}$

Step 5

Cancel the common factor of $q^{5}$ and $q$ .

Factor $q$ out of $q^{5} r^{8}$ .

$\frac{q (q^{4} r^{8})}{p q}$

Cancel the common factors.

Factor $q$ out of $p q$ .

$\frac{q (q^{4} r^{8})}{q p}$

Cancel the common factor.

$\frac{q (q^{4} r^{8})}{q p}$

Rewrite the expression.

$\frac{q^{4} r^{8}}{p}$