(27/8)^-2/3 As A Fraction

Jasonbradley

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Jun 16, 2024

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Simplifying (27/8)^(-2/3) as a Fraction

This problem involves simplifying a fractional exponent. Let's break down the steps:

Understanding Fractional Exponents

A fractional exponent like (-2/3) indicates both a root and a power. The denominator (3 in this case) represents the root (cube root), and the numerator (-2) represents the power.

Applying the Rules

1. Reciprocal: A negative exponent indicates a reciprocal. Therefore, (27/8)^(-2/3) is the same as (8/27)^(2/3).

2. Cube Root: We take the cube root of both the numerator and denominator: ∛8 = 2 and ∛27 = 3.

3. Squaring: We square the resulting numbers: 2² = 4 and 3² = 9.

Final Result

By applying these steps, we get (27/8)^(-2/3) = (8/27)^(2/3) = (2/3)² = 4/9.