# How do you use the laws of exponents to simplify the expression -(9^2 x^-2 y^2)^-1/(9^4 x^4 y^4)^-3?

##### 1 Answer
Mar 5, 2018

$- {9}^{10} {x}^{14} {y}^{10}$

#### Explanation:

When you see a negative exponent, it means that the exponent's "home" is on the other level

${x}^{-} 5$ wants to live on the bottom level, like this: $\frac{1}{x} ^ 5$

$\frac{1}{x} ^ - 3$ wants to live on the top level. like this: ${x}^{3}$

Based off of that, let's rewrite this expression

$- \left({9}^{2} {x}^{2} - 2 {y}^{2}\right) - \frac{1}{{9}^{4} {x}^{4} {y}^{4}} ^ - 3$

$- {\left({9}^{4} {x}^{4} {y}^{4}\right)}^{3} / \left({9}^{2} {x}^{-} 2 {y}^{2}\right)$

Let's distribute that $3$

$- \frac{{9}^{12} {x}^{12} {y}^{12}}{{9}^{2} {x}^{-} 2 {y}^{2}}$

Now we can move that ${x}^{-} 2$ up to it's "home"

$- \frac{{9}^{12} {x}^{12} {x}^{2} {y}^{12}}{{9}^{2} {y}^{2}}$

Now comes the fun part. When we are dividing variables, we subtract their exponents

$- {9}^{10} {x}^{14} {y}^{10}$