(-27)^(2/3)

Jasonbradley

2 min read

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Jun 16, 2024

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Understanding (-27)^(2/3)

The expression (-27)^(2/3) represents a fractional exponent, which indicates both raising to a power and taking a root. Let's break it down:

Fractional Exponents

The fraction 2/3 signifies that we need to perform two operations:

1. Cube root (3 in the denominator): Find the number that, when multiplied by itself three times, equals -27. This is -3 since (-3)(-3)(-3) = -27.
2. Squaring (2 in the numerator): Square the result obtained in step 1, which is (-3)^2 = 9.

Calculation

Therefore, (-27)^(2/3) is calculated as follows:

1. Cube root of -27: ∛(-27) = -3
2. Square of -3: (-3)^2 = 9

Solution

Therefore, (-27)^(2/3) = 9.

Key Points

• Fractional exponents: a^(m/n) = (n√a)^m
• Cube root: The cube root of a number is the number that, when multiplied by itself three times, equals the original number.
• Negative base: When taking an odd root of a negative number, the result is negative.
• Even exponent: Squaring a negative number results in a positive number.