# How do you simplify 1/ x^-4?

May 19, 2015

One law of exponent states that ${a}^{-} n = \frac{1}{a} ^ n$.

In this case, $\frac{1}{x} ^ - 4 = {\left({x}^{-} 4\right)}^{-} 1$

But another law of exponent states that ${\left({a}^{n}\right)}^{m} = {a}^{n \cdot m}$

Thus,

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

Finally, $\frac{1}{x} ^ - 4 = {x}^{4}$