The problem asks to evaluate $(-8)^{\frac{2}{3}}$.

AlgebraExponentsRadicalsSimplification
2025/5/19

1. Problem Description

The problem asks to evaluate (8)23(-8)^{\frac{2}{3}}.

2. Solution Steps

We need to evaluate the expression (8)23(-8)^{\frac{2}{3}}. We can rewrite this expression as:
(8)23=((8)13)2(-8)^{\frac{2}{3}} = ((-8)^{\frac{1}{3}})^2
First, we find the cube root of -8:
(8)13=83=2(-8)^{\frac{1}{3}} = \sqrt[3]{-8} = -2
Then, we square the result:
(2)2=(2)×(2)=4(-2)^2 = (-2) \times (-2) = 4
Therefore, (8)23=4(-8)^{\frac{2}{3}} = 4.

3. Final Answer

4

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