Problem 86 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: Get the answer

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