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Chapter 0: Problem 86

Evaluate each expression without using a calculator. $$27^{\frac{1}{3}}$$

Short Answer

Expert verified
The expression \(27^{\frac{1}{3}}\) equals 3.

Step by step solution

01

Understanding the task

The given expression \(27^{\frac{1}{3}}\) represents the cube root of 27. Finding cube root is like the inverse operation of cubing a number. The main task here is to find a number that, when cubed, would give 27.
02

Calculating cube root

To calculate the cube root, think of a number which will give 27 when it is raised to the power 3. The number 3 comes to mind because \(3^3\) (3 cubed or 3 raised to the power 3) equals 27.
03

Get the answer

Therefore, \(27^{\frac{1}{3}}\) equals 3 since 3 is the number that, when cubed, equals 27.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$7^{\frac{1}{2}} \cdot 7^{\frac{1}{2}}=49$$

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Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{-\frac{5}{4} y^{\frac{1}{3}}}}{x^{-\frac{3}{4}}}\right)^{-6} $$

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