Simplify (15p^-4q^-6)/(-20p^-12q^-3)

$\frac{15 p^{- 4} q^{- 6}}{- 20 p^{- 12} q^{- 3}}$

Step 1

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

$\frac{15 p^{- 4}}{- 20 p^{- 12} q^{- 3} q^{6}}$

Step 2

Multiply $q^{- 3}$ by $q^{6}$ by adding the exponents.

Move $q^{6}$ .

$\frac{15 p^{- 4}}{- 20 p^{- 12} (q^{6} q^{- 3})}$

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

$\frac{15 p^{- 4}}{- 20 p^{- 12} q^{6 - 3}}$

Subtract $3$ from $6$ .

$\frac{15 p^{- 4}}{- 20 p^{- 12} q^{3}}$

Step 3

Move $p^{- 12}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{15 p^{- 4} p^{12}}{- 20 q^{3}}$

Step 4

Multiply $p^{- 4}$ by $p^{12}$ by adding the exponents.

Move $p^{12}$ .

$\frac{15 (p^{12} p^{- 4})}{- 20 q^{3}}$

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

$\frac{15 p^{12 - 4}}{- 20 q^{3}}$

Subtract $4$ from $12$ .

$\frac{15 p^{8}}{- 20 q^{3}}$

Step 5

Cancel the common factor of $15$ and $- 20$ .

Factor $5$ out of $15 p^{8}$ .

$\frac{5 (3 p^{8})}{- 20 q^{3}}$

Cancel the common factors.

Factor $5$ out of $- 20 q^{3}$ .

$\frac{5 (3 p^{8})}{5 (- 4 q^{3})}$

Cancel the common factor.

$\frac{5 (3 p^{8})}{5 (- 4 q^{3})}$

Rewrite the expression.

$\frac{3 p^{8}}{- 4 q^{3}}$

Step 6

Move the negative in front of the fraction.

$- \frac{3 p^{8}}{4 q^{3}}$