# How do you simplify 42 x^11 y^-5?

May 23, 2015

We can use two exponential properties here.

First, ${a}^{-} n = \frac{1}{a} ^ n$.

Now, we have $\frac{42 {x}^{11}}{y} ^ 5$

We also know that ${a}^{n} \cdot {a}^{m} = {a}^{n + m}$, so we can rewrite

$\frac{42 {x}^{5} {x}^{6}}{y} ^ 5$

Another property indicates that ${a}^{n} / {b}^{n} = {\left(\frac{a}{b}\right)}^{n}$, thus, finally,

$\left(42 {x}^{6}\right) {\left(\frac{x}{y}\right)}^{5}$