Question

Represent the following expressions as a power of the number a where a ‡0.

((a−²)-¹)-¹ ÷ (a÷a¯¹)²

Answer 1

Properties we are going to use :
1. (a^m)^n = a^mn
2. a^m : a^n = a^(m-n)

((a^-2)^-1)^-1 = (a^(-2 x -1))^-1 = (a^2)^-1 = a^-2

(a : a^-1)^2 = (a^1 - (-1))^2 = (a^2)^2 = a^4

Therefore, the expression is simplified down to a^-2 : a^4

a^-2 : a^4 = a^(-2 - 4) = a^-6.