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Chapter 10: Problem 11

A student incorrectly evaluated \(27^{1 / 3}\) as \(9 .\) Evaluate \(27^{1 / 3}\) correctly.

Short Answer

Expert verified
The correct value of \(27^{1/3}\) is 3.

Step by step solution

01

Understand the problem

The given exercise involves evaluating the expression \(27^{1/3}\). This means finding the cube root of 27.
02

Rewrite the expression

The expression \(27^{1/3}\) can be rewritten as \(\root{3}{27}\), which asks for the number that, when raised to the power of 3, gives 27.
03

Evaluate the cube root

Identify the number that, when cubed, equals 27: \(3^3 = 27\). Therefore, the cube root of 27 is 3.
04

Confirm the result

To confirm the result, cube 3 to see if it equals 27: \(3^3 = 3 \times 3 \times 3 = 27\). This verification confirms that \(27^{1/3} = 3\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Exponentiation
Exponentiation is a mathematical operation that involves raising a number to the power of another number. It is represented as

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