Question

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

Answer 1

$a^{-2}$

Explanation

let's remember some properties of the exponents

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

Step 1

$(\frac{a}{a^2})^2$

a) apply the fourth property

$\begin{gathered} (\frac{a}{a^2})^2 \\ (a^{1-2})^2 \\ (a^{-1})^2 \end{gathered}$

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