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Chapter 0: Problem 87

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

Short Answer

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

Step by step solution

01

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, \(\sqrt[3]{125} = 5\)
02

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 \(5^2 = 25\).
03

Final Answer

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

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Most popular questions from this chapter

In Exercises 136鈥�143, determine whether each statement is true or false. If the statement is false, make the necessary change(s) toproduce a true statement. $$4^{-2}<4^{-3}$$

Explain how to convert from decimal to scientific notation and give an example.

Explain the power rule for exponents. Use \(\left(3^{2}\right)^{4}\) in your explanation.

Evaluate each expression without using a calculator. $$8^{\frac{2}{3}}$$

Simplify using properties of exponents. $$\left(x^{\frac{2}{3}}\right)^{3}$$
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