(-27)^5/3

Jasonbradley

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Jun 16, 2024

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Simplifying (-27)^(5/3)

This problem involves simplifying a number raised to a fractional exponent. Let's break it down step-by-step:

Understanding Fractional Exponents

A fractional exponent like 5/3 represents both a power and a root.

• The numerator (5) indicates the power to which the base is raised.
• The denominator (3) indicates the root to be taken.

Therefore, (-27)^(5/3) can be interpreted as:

• The cube root of -27, raised to the power of 5.

Calculation

1. Find the cube root of -27: The cube root of -27 is -3, because -3 x -3 x -3 = -27.

2. Raise the cube root to the power of 5: (-3)^5 = -3 x -3 x -3 x -3 x -3 = -243.

Answer

Therefore, (-27)^(5/3) is equal to -243.