Simplify the expression $\frac{2^3 \times 2^{-3}}{2^2}$.

1. Problem Description

Simplify the expression $\frac{2^3 \times 2^{-3}}{2^2}$.

2. Solution Steps

First, we simplify the numerator using the rule $a^m \times a^n = a^{m+n}$.

$2^3 \times 2^{-3} = 2^{3 + (-3)} = 2^0$

We know that $a^0 = 1$ for any non-zero $a$. Thus, $2^0 = 1$.

So, the expression becomes $\frac{1}{2^2}$.

Since $2^2 = 2 \times 2 = 4$, the expression simplifies to $\frac{1}{4}$.

3. Final Answer

$\frac{1}{4}$