(-27)^-4/3

Jasonbradley

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Jun 16, 2024

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Simplifying (-27)^-4/3

This article will guide you through the process of simplifying the expression (-27)^-4/3.

Understanding the Properties

To simplify this expression, we need to understand the following properties:

• Negative exponents: A negative exponent indicates the reciprocal of the base raised to the positive value of the exponent. For example, x^-n = 1/x^n.
• Fractional exponents: A fractional exponent represents a root. For example, x^(m/n) = (n√x)^m. This means the nth root of x is raised to the power of m.

Simplifying the Expression

Let's break down the expression step-by-step:

1. Dealing with the negative exponent: (-27)^-4/3 = 1 / (-27)^(4/3)

2. Applying the fractional exponent: 1 / (-27)^(4/3) = 1 / (∛(-27))^4

3. Finding the cube root: 1 / (∛(-27))^4 = 1 / (-3)^4

4. Evaluating the power: 1 / (-3)^4 = 1 / 81

Therefore, (-27)^-4/3 = 1/81.

Conclusion

By understanding the properties of exponents, we were able to simplify the expression (-27)^-4/3 to 1/81. This example demonstrates how to handle both negative and fractional exponents in a clear and methodical manner.