Question

(a/ a raised to the 2 power ) raised to the -2 power

Answer 1

`a^(-2)`

Step-by-step explanation

let's remember some properties of the exponents

`\begin{gathered} a^m\cdot a^n=a^(m+n) \\ ((a)/(b))^m=(a^m)/(b^m) \\ (1)/(a^m)=a^(-1) \\ (a^m)/(a^n)=a^(m-n) \\ (a^m)^n=a^(m\cdot n) \end{gathered}`

Step 1

`((a)/(a^2))^2`

a) apply the fourth property

`\begin{gathered} ((a)/(a^2))^2 \\ (a^(1-2))^2 \\ (a^(-1))^2 \end{gathered}`

b) Now, apply the fifth property

`\begin{gathered} (a^(-1))^2 \\ a^(-1\cdot2) \\ a^(-2) \end{gathered}`

so, the answer is

`a^(-2)`

I hope this helps you