Math Problem Statement

Simplify

Simplify \(\left( -\frac{1}{8} \right)^{-\frac{2}{3}}\)

Solution

The simplified form of the expression (−18)−23\left( -\frac{1}{8} \right)^{-\frac{2}{3}} is:

−4⋅(−1)13-4 \cdot (-1)^{\frac{1}{3}}

This result includes a cube root of −1-1, which is represented as ((-1)^{1/3

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Roots of Negative Numbers

Formulas

a^{-b} = \frac{1}{a^b}
Cube root: \sqrt[3]{x} = x^{1/3}

Theorems

Exponentiation Rule
Cube Root of Negative Numbers

Suitable Grade Level

Grades 9-11

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