Simplify (28p^9q^-5)/(12p^-6q^7)

$\frac{28 p^{9} q^{- 5}}{12 p^{- 6} q^{7}}$

Move $q^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{28 p^{9}}{12 p^{- 6} q^{7} q^{5}}$

Multiply $q^{7}$ by $q^{5}$ by adding the exponents.

Move $q^{5}$ .

$\frac{28 p^{9}}{12 p^{- 6} (q^{5} q^{7})}$

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

$\frac{28 p^{9}}{12 p^{- 6} q^{5 + 7}}$

Add $5$ and $7$ .

$\frac{28 p^{9}}{12 p^{- 6} q^{12}}$

Move $p^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{28 p^{9} p^{6}}{12 q^{12}}$

Multiply $p^{9}$ by $p^{6}$ by adding the exponents.

Move $p^{6}$ .

$\frac{28 (p^{6} p^{9})}{12 q^{12}}$

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

$\frac{28 p^{6 + 9}}{12 q^{12}}$

Add $6$ and $9$ .

$\frac{28 p^{15}}{12 q^{12}}$

Cancel the common factor of $28$ and $12$ .

Factor $4$ out of $28 p^{15}$ .

$\frac{4 (7 p^{15})}{12 q^{12}}$

Cancel the common factors.

Factor $4$ out of $12 q^{12}$ .

$\frac{4 (7 p^{15})}{4 (3 q^{12})}$

Cancel the common factor.

$\frac{4 (7 p^{15})}{4 (3 q^{12})}$

Rewrite the expression.

$\frac{7 p^{15}}{3 q^{12}}$