(-64)^4/3

Jasonbradley

2 min read

·

Jun 16, 2024

9

Share

Simplifying (-64)^(4/3)

The expression (-64)^(4/3) represents a combination of a negative base, a fractional exponent, and a power. Let's break it down to understand how to simplify it:

Understanding Fractional Exponents

A fractional exponent like (4/3) can be interpreted as a combination of a root and a power:

• The denominator (3) indicates the root: In this case, it's a cube root (∛).
• The numerator (4) indicates the power: We need to raise the result of the root to the power of 4.

Step-by-Step Simplification

1. Cube root of -64: Find the number that, when multiplied by itself three times, equals -64. This is -4, since (-4) * (-4) * (-4) = -64.

   Therefore, ∛(-64) = -4.

2. Raising to the power of 4: We now have (-4)^4. This means we multiply -4 by itself four times: (-4) * (-4) * (-4) * (-4) = 256.

The Final Result

Therefore, (-64)^(4/3) simplifies to 256.