# How do you simplify (g^2/h)/(g^5/h^2)?

Mar 19, 2017

$\frac{\frac{{g}^{2}}{h}}{\frac{{g}^{5}}{{h}^{2}}} = \textcolor{g r e e n}{\frac{h}{{g}^{3}}}$

#### Explanation:

Division is equivalent to multiplication by the (multiplicative) inverse.

So $\frac{\frac{{g}^{2}}{h}}{\frac{{g}^{5}}{{h}^{2}}}$

is equivalent to $\left(\frac{{g}^{2}}{h}\right) \times \left(\frac{{h}^{2}}{{g}^{5}}\right)$

$\textcolor{w h i t e}{\text{XXX}} \left(\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{{g}^{2}}}}}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{h}}}}\right) \times \left(\frac{\textcolor{b l u e}{{\cancel{\textcolor{b l a c k}{{h}^{2}}}}^{h}}}{\textcolor{red}{{\cancel{\textcolor{b l a c k}{{g}^{5}}}}_{{g}^{3}}}}\right)$

$\textcolor{w h i t e}{\text{XXX}} = \frac{h}{{g}^{3}}$