How do you divide #(x^4y^-2) /(x^-3y^5)#?

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Answer 1 · 2018-03-23T00:50:54

#(x/y)^7#

Division of like-terms will powers is equivalent to writing the term with the difference of the powers.

#=>(x^4y^(-2))/(x^(-3)y^5)#

We have #x^4# in the numerator and #x^(-3)# in the denominator. This means we can write #x^(4-(-3))=x^7# in the numerator.

We have #y^(-2)# in the numerator and #y^5# in the denominator. This means we can write #y^(-2-5) = y^(-7)# in the numerator.

Hence:

#=>(x^4y^(-2))/(x^(-3)y^5) = x^7y^(-7)#

Or, equilavently:

#=>x^7y^(-7) = x^7/y^(7) = (x/y)^7#