# How do you simplify (g^0h^7j^-2)/(g^-5h^0j^-2)?

Mar 2, 2017

See the entire simplification process below:

#### Explanation:

The first step I would take is to rewrite this expression as:

$\left({g}^{0} / {g}^{-} 5\right) \left({h}^{7} / {h}^{0}\right) \left({j}^{-} \frac{2}{j} ^ - 2\right)$

We can use this rule of exponents to simplify this expression:

${a}^{\textcolor{red}{0}} = 1$

And, we know $\frac{x}{x} = 1$ therefore ${J}^{-} \frac{2}{j} ^ - 2 = 1$

So we can again rewrite the expression as:

$\left(\frac{1}{g} ^ - 5\right) \left({h}^{7} / 1\right) \left(1\right) = {h}^{7} / {g}^{-} 5$

We can eliminate the negative exponent by using this rule for exponents: $\frac{1}{x} ^ \textcolor{red}{a} = {x}^{\textcolor{red}{- a}}$

${h}^{7} / \left({g}^{\textcolor{red}{- 5}}\right) = {h}^{7} {g}^{\textcolor{red}{- - 5}} = {h}^{7} {g}^{5}$