(−64)4/3

Jasonbradley

2 min read

·

Jun 17, 2024

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Understanding (-64)^4/3

The expression (-64)^4/3 might look intimidating at first, but it's actually quite simple to understand once you break it down. Let's explore it step-by-step:

Fractional Exponents

Fractional exponents represent a combination of roots and powers. The denominator of the fraction indicates the root to be taken, and the numerator indicates the power to be applied.

In our case, we have:

• Denominator (3): This means we need to find the cube root of -64.
• Numerator (4): This means we need to raise the result to the power of 4.

Solving the Expression

1. Cube Root: The cube root of -64 is -4, because -4 x -4 x -4 = -64.
2. Power: Now, we raise -4 to the power of 4: (-4)⁴ = (-4) x (-4) x (-4) x (-4) = 256.

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

Key Points

• Fractional exponents are a combination of roots and powers.
• The denominator indicates the root, and the numerator indicates the power.
• Remember that the cube root of a negative number is also negative.

By understanding the concept of fractional exponents and applying the steps, we can easily solve even complex-looking expressions like (-64)^4/3.