(-64) 2/3

2 min read Jun 17, 2024
(-64) 2/3

Understanding (-64)<sup>2/3</sup>

The expression (-64)<sup>2/3</sup> might seem daunting at first, but it's actually a fairly straightforward calculation once you understand the properties of exponents and roots. Here's a breakdown:

Fractional Exponents

Fractional exponents represent a combination of powers and roots. The numerator of the fraction indicates the power, while the denominator indicates the root.

In this case, 2/3 means we need to find the cube root (3 in the denominator) of -64 and then square it (2 in the numerator).

Solving the Expression

  1. Cube Root: The cube root of -64 is -4 because -4 * -4 * -4 = -64.
  2. Square: Squaring -4 gives us (-4)<sup>2</sup> = 16.

Therefore, (-64)<sup>2/3</sup> = 16.

Key Points to Remember

  • Negative Base: When dealing with a negative base and a fractional exponent where the denominator is odd (like in our case), the result will be negative.
  • Fractional Exponents and Roots: Understanding the relationship between fractional exponents and roots is crucial for solving these types of expressions.
  • Calculator: While the process is simple, calculators can be used to verify your calculations.

By breaking down the expression and understanding the properties of exponents and roots, you can confidently solve (-64)<sup>2/3</sup> and similar expressions.

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