How do you simplify and write (4w^-6x^2)^2(4w−6x2)2 with positive exponents?

1 Answer
ProfLayton
Apr 16, 2016

First of all, let's remove that big squared symbol around the whole equation. Note: You will need to know two things, (ab)^n=a^n*b^n(ab)n=an⋅bn, and (a^m)^n=a^(mn)(am)n=amn

(4*w^-6*x^2)^2 = 4^2*w^(-6*2)*x^(2*2)(4⋅w−6⋅x2)2=42⋅w−6⋅2⋅x2⋅2
= 16*w^(-12)*x^(4)=16⋅w−12⋅x4

But the question asks for all exponents (those smaller, higher numbers) to be positive. For this we need another piece of knowledge: a^-n = 1/a^na−n=1an

=(16*w^4)/x^12=16⋅w4x12

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