Question

Simplify the expression 4^-2*2^6 over 4^2*2^2

Answer 1

$4=2^2\\------------\\\\\dfrac{4^{-2}\cdot2^6}{4^2\cdot2^2}=\dfrac{(2^2)^{-2}\cdot2^6}{(2^2)^2\cdot2^2}=\dfrac{2^{-4}\cdot2^6}{2^4\cdot2^2}=\dfrac{2^{-4+6}}{2^4\cdot2^2}=\dfrac{2^2}{2^4\cdot2^2}=\dfrac{1}{2^4}=\dfrac{1}{16}\\\\---------------------\\\\Used:\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}$