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:

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

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