How do you simplify (\frac { 2x y \cdot 2y x ^ { 0} } { ( - 2x y ^ { 4} ) ^ { 2} } ) ^ { - 3}?

1 Answer
Sep 11, 2017

x^3y^18

Explanation:

A few things about fractions and exponents we need to keep in mind:

1) (a/b)^-x=(b/a)^x

2) a^x/a^y=a^(x-y)

3) a^0=1

4) (ab)^x=a^xb^x

5) (a^x)^y=a^(x*y)

So, with that, we have the following:

((2xy*2yx^0)/(-2xy^4)^2)^-3

((-2xy^4)^2/(2xy*2yx^0))^3larr using property 1

((4x^2y^8)/(2xy*2y))^3larr property 4 on top and 3 on the bottom

((4x^2y^8)/(4xy^2))^3larr multiplying out the bottom

Now we can divide the top by the bottom using property 2

((cancel(4)x^cancel(2)y^cancel(8))/(cancel(4)cancel(x)cancel(y^2)))^3

As you can see, all of the bottom cancels out leaving us with:

(xy^6)^3

Now we just use property 5 to get us:

x^3y^(6*3)

x^3y^18