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(-1/8)^1/3

2 min read Jun 16, 2024
(-1/8)^1/3

Understanding (-1/8)^(1/3)

The expression (-1/8)^(1/3) represents the cube root of -1/8. Let's break down how to solve this:

Understanding Cube Roots

A cube root of a number is a value that, when multiplied by itself three times, equals the original number. For example, the cube root of 8 is 2 because 2 * 2 * 2 = 8.

Finding the Cube Root of -1/8

  • Step 1: Consider the sign. Since the base (-1/8) is negative, the cube root will also be negative.
  • Step 2: Find the cube root of the absolute value. The absolute value of -1/8 is 1/8. The cube root of 1/8 is 1/2 because (1/2) * (1/2) * (1/2) = 1/8.

Therefore, (-1/8)^(1/3) = -1/2.

Key Points

  • Fractional exponents represent roots. The denominator of the fractional exponent indicates the type of root.
  • Negative bases and odd roots result in negative values. This is because a negative number multiplied by itself an odd number of times results in a negative number.

By understanding these concepts, you can confidently solve expressions involving fractional exponents and cube roots.

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