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Chapter 0: Problem 85

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

Short Answer

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

Step by step solution

01

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.
02

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.
03

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.

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Most popular questions from this chapter

a. Simplify: \(21 x+10 x\) b. Simplify: \(21 \sqrt{2}+10 \sqrt{2}\)

Will help you prepare for the material covered in the next section.Exercises \(144-146\) will help you prepare for the material covered in the next section. Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. $$ \frac{x^{2}+6 x+5}{x^{2}-25} $$

Simplify using properties of exponents. $$\frac{20 x^{\frac{1}{2}}}{5 x^{4}}$$

Find all integers b so that the trinomial can be factored. $$ x^{2}+b x+15 $$

What difference is there in simplifying \(\sqrt[3]{(-5)^{3}}\) and \(\sqrt[4]{(-5)^{4}} ?\)
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