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

AlgebraExponentsSimplificationFractions
2025/3/8

1. Problem Description

Simplify the expression 23×2322\frac{2^3 \times 2^{-3}}{2^2}.

2. Solution Steps

First, we simplify the numerator using the rule am×an=am+na^m \times a^n = a^{m+n}.
23×23=23+(3)=202^3 \times 2^{-3} = 2^{3 + (-3)} = 2^0
We know that a0=1a^0 = 1 for any non-zero aa. Thus, 20=12^0 = 1.
So, the expression becomes 122\frac{1}{2^2}.
Since 22=2×2=42^2 = 2 \times 2 = 4, the expression simplifies to 14\frac{1}{4}.

3. Final Answer

14\frac{1}{4}

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