Problem 87 - College Algebra

Question

Evaluate each expression without using a calculator. $$125^{\frac{2}{3}}$$

Step-by-Step Solution

Answer

Therefore, \(125^{2/3}\) = 25

Step 1: Calculate the Cube Root

Firstly, take the cube root of 125. The cube root of a number \(x\) is a value that, when cubed (multipled by itself twice), gives the original number \(x\). Therefore, we shall find a number which results in 125 when we multiply it by itself twice. This turns out to be 5, because \(5 * 5 * 5 = 125\). Thus, \(\sqrt[3]{125} = 5\)

Step 2: Square the Root

Next, we take the result from Step 1 and square it. Squaring a number means multiplying it by itself. Therefore, we do \(5^2 = 25\).

Step 3: Final Answer

After executing the operations of the fractional exponent in order, we obtain the final result.