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

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Answer 1 · 2017-09-11T05:38:38

#x^3y^18#

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#