(-1/27)^-2/3

Jasonbradley

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Jun 16, 2024

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Simplifying (-1/27)^(-2/3)

This article will guide you through simplifying the expression (-1/27)^(-2/3).

Understanding the Properties of Exponents

Before diving into the simplification, let's refresh our understanding of key exponent properties:

• Negative Exponent: x⁻ⁿ = 1/xⁿ
• Fractional Exponent: x^(m/n) = (ⁿ√x)ᵐ

Applying the Properties to Simplify the Expression

1. Dealing with the Negative Exponent: Using the negative exponent property, we can rewrite the expression as: (-1/27)^(-2/3) = 1 / (-1/27)^(2/3)

2. Simplifying the Fractional Exponent: Now, applying the fractional exponent property: 1 / (-1/27)^(2/3) = 1 / (∛(-1/27))²

3. Calculating the Cube Root: The cube root of -1/27 is -1/3. 1 / (∛(-1/27))² = 1 / (-1/3)²

4. Squaring the Result: Squaring -1/3 gives us 1/9. 1 / (-1/3)² = 1 / (1/9)

5. Dividing by a Fraction: Dividing by a fraction is equivalent to multiplying by its reciprocal. 1 / (1/9) = 1 * 9 = 9

Final Answer

Therefore, (-1/27)^(-2/3) = 9.