# What is the quotient of -18x^-2+27x^-2-72x^-8 and 9x?

Nov 24, 2016

${x}^{-} 3 - 8 {x}^{-} 9$ or $\frac{1}{x} ^ 3 - \frac{8}{x} ^ 9$

#### Explanation:

This problem can be written as, what is:

$\frac{- 18 {x}^{-} 2 + 27 {x}^{-} 2 - 72 {x}^{-} 8}{9 x}$

First, we can combine like terms:

$\frac{\left(- 18 + 27\right) {x}^{-} 2 - 72 {x}^{-} 8}{9 x}$

$\frac{9 {x}^{-} 2 - 72 {x}^{-} 8}{9 x}$

We can now rewrite this as two separate fractions:

$\frac{9 {x}^{-} 2}{9 x} - \frac{72 {x}^{-} 8}{9 x}$

$\left(\frac{9}{9}\right) \left({x}^{-} \frac{2}{x} ^ 1\right) - \left(\frac{72}{9}\right) \left({x}^{-} \frac{8}{x} ^ 1\right)$

Dividing the constants and using the rules of exponents we get:

$1 \left({x}^{- 2 - 1}\right)$ - 8(x^(-8 - 1))#

${x}^{-} 3 - 8 {x}^{-} 9$