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(-64)^-1/3

2 min read Jun 16, 2024
(-64)^-1/3

Simplifying (-64)^(-1/3)

This problem involves simplifying an expression with a negative base and a fractional exponent. Let's break down the steps:

Understanding Fractional Exponents

A fractional exponent like (-1/3) represents both a root and a power.

  • The denominator (3) indicates the type of root. In this case, it's a cube root.
  • The numerator (-1) indicates the power. Here, it's raising to the power of -1, which means finding the reciprocal.

Solving the Expression

  1. Cube Root: Find the cube root of -64. The cube root of -64 is -4 because (-4) * (-4) * (-4) = -64.
  2. Reciprocal: Take the reciprocal of the result from step 1. The reciprocal of -4 is -1/4.

Therefore, (-64)^(-1/3) = -1/4.

Key Points to Remember

  • Negative Bases: When dealing with negative bases and fractional exponents, remember to consider the sign of the result. In this case, a negative base raised to an odd power results in a negative outcome.
  • Reciprocal: Raising a number to the power of -1 is the same as finding its reciprocal.

Let me know if you'd like to explore other examples with fractional exponents!

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