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

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Answer 1 · 2018-06-10T23:46:30

$\frac{1}{4 x^{5}}$ $1/(4x^5)$

We can rewrite our expression as

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

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

Next, we will leverage the exponent property

$\frac{x^{a}}{x^{b}} = x^{a - b}$ $(x^a)/(x^b)=x^(a-b)$

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

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

Which simplifies further to

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

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

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

Hope this helps!

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