# How do you simplify \frac { x ^ { - 1 } } { 4 x ^ { 4 } }?

Jun 10, 2018

$\frac{1}{4 {x}^{5}}$

#### Explanation:

We can rewrite our expression as

$\frac{1}{4} \left({x}^{- 1} / {x}^{4}\right)$

And now, all we have to pay attention to is the variables.

Next, we will leverage the exponent property

$\frac{{x}^{a}}{{x}^{b}} = {x}^{a - b}$

All this is saying is that if we have the same base, we subtract the exponents. Applying this, we get

$\frac{1}{4} \left({x}^{- 1 - 4}\right)$

Which simplifies further to

$\frac{1}{4} {x}^{-} 5$

If the negative exponent bothers you, we can easily make it positive by bringing it to the denominator. We'll get

$\frac{1}{4} {x}^{-} 5 = \frac{1}{4 {x}^{5}}$

Hope this helps!