How do you simplify ((2x^-6)/(7y^-3))^-3?

2 Answers
Topscooter
Jan 9, 2016

(343x^18)/(8y^9)

Explanation:

A negative power x^(-n) can be seen as x^(n^(-1)). We know that x^(-1) = 1/x so x^(n^(-1)) = 1/x^n, hence the following simplyfictations : 2x^-6 = 2/x^6 and 7y^-3 = 7/y^3

So ((2x^-6)/(7y^-3))^(-3) = ((2/x^6)/(7/y^3))^(-3) = ((2/x^6)*(y^3/7))^(-3).

We do what we did before : ((2/x^6)*(y^3/7))^(-3) = (x^6/2*7/y^3)^3 = (343x^18)/(8y^9)

Tony B
Jan 9, 2016

A slightly different way or writing the working out!

(343x^18)/(8y^9)

Explanation:

Given: ( (2x^(-6))/(7y^(-3)))^(-3)

First consider inside the brackets:

Known that color(white)(..)2x^(-6) -> 2/(x^6)" and that " 1/(7y^(-3)) ->y^3/7

So we have 2/x^6xxy^3/7= (2y^3)/(7x^6)

Now put this back into the brackets giving

((2y^3)/(7x^6))^(-3) = ((7x^6)/(2y^3))^3

=(343x^18)/(8y^9)

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