(−64)23

Jasonbradley

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Jun 17, 2024

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Understanding (-64)^2/3

The expression (-64)^2/3 might seem intimidating, but it's a straightforward calculation once we break it down. Let's explore the concept:

Fractional Exponents

A fractional exponent represents both a root and a power. In our case, the exponent 2/3 signifies taking the cube root and then squaring the result.

Applying the Principles

1. Cube Root: The cube root of -64 is -4, as -4 x -4 x -4 = -64.
2. Squaring: We square the result of the cube root, (-4)^2 = 16.

Therefore, (-64)^2/3 = 16.

Key Takeaways

• Fractional exponents combine roots and powers.
• The denominator of the fraction indicates the root to be taken.
• The numerator indicates the power to be applied.

By understanding these principles, you can tackle more complex expressions with fractional exponents confidently.