Problem 85 - College Algebra

Question

Evaluate each expression without using a calculator. $$8^{\frac{1}{3}}$$

Step-by-Step Solution

Answer

The result of the expression \(8^{\frac{1}{3}}\) is 2.

Step 1: Interpret

We first need to understand what \(8^{\frac{1}{3}}\) means. In this case, the exponent is \(\frac{1}{3}\), which is the same as taking the cube root of 8.

Step 2: Apply the Concept of Cube Root

Taking a cube root means finding the number that, when multiplied by itself twice (cubed), gives the original number. In other words, we want to find a number that, when we multiply it by itself (\(x*x*x\)), gives 8.

Step 3: Find the Cube Root

It's known that \(2*2*2=8\). So, the cube root of 8 (or \(8^{\frac{1}{3}}\)) is 2.