# How do you simplify \frac { - 6p ^ { 4} q ^ { 6} s ^ { 2} } { 10s ^ { 2} p ^ { 5} q ^ { 2} }?

Feb 16, 2017

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

#### Explanation:

$\frac{- 6 {p}^{4} {q}^{6} {s}^{2}}{10 {s}^{2} {p}^{5} {q}^{2}}$

when you divide powers you subtract them

$\frac{- 6 {q}^{6 - 2} {s}^{2 - 2}}{10 {p}^{5 - 4}} = \frac{- 6 {q}^{4} \left(1\right)}{10 p} = \textcolor{p u r p \le}{\frac{- 3 {q}^{4}}{5 p}}$

you can also subtract all the powers in the numerator or denominator if you want, it doesn't matter because the negative-exponent rule would fix that
$\frac{- 6 {p}^{4 - 5} {q}^{6 - 2} {s}^{2 - 2}}{10} = \frac{- 6 {p}^{-} 1 {q}^{4} \left(1\right)}{10} = \frac{- 3 {q}^{4}}{5 p}$