# How do you simplify (x^9z^(-3))/(x^6z^2)?

Mar 28, 2016

$= {x}^{\textcolor{b l u e}{3}} / {z}^{\textcolor{b l u e}{5}}$

#### Explanation:

(x^9 z ^-3) / (x^6 z ^2

$= \left({x}^{9} / {x}^{6}\right) \cdot \left({z}^{-} \frac{3}{z} ^ 2\right)$

• As per property:
color(blue)(a^m / a ^n = a ^(m-n)

 = x^ color(blue)((9 - 6) ) * z ^ color(blue)((-3 - 2)

$= {x}^{\textcolor{b l u e}{3}} \cdot {z}^{\textcolor{b l u e}{- 5}}$

$= {x}^{\textcolor{b l u e}{3}} {z}^{\textcolor{b l u e}{- 5}}$

• As per property:
color(blue)(1/a^-1 = a , applying the same to $z$

$= {x}^{\textcolor{b l u e}{3}} / {z}^{\textcolor{b l u e}{5}}$