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#?

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Answer 1 · 2018-03-05T06:31:49

#-9^10 x^14 y^10#

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: #1/x^5#

#1/x^-3# wants to live on the top level. like this: #x^3#

Based off of that, let's rewrite this expression

#-(9^2x^2-2y^2)-1/(9^4x^4y^4)^-3#

#-(9^4x^4y^4)^3/(9^2x^-2y^2)#

Let's distribute that #3#

#-(9^12x^12y^12)/(9^2x^-2y^2)#

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

#-(9^12x^12x^2y^12)/(9^2y^2)#

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

#-9^10 x^14 y^10#