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Chapter 0: Problem 69

Simplify the radical expressions if possible. $$\sqrt[3]{x^{4}}$$

Short Answer

Expert verified
\( x * \sqrt[3]{x} \)

Step by step solution

01

Breaking Down the Expression

We break down the expression \( \sqrt[3]{x^{4}} \) into \( \sqrt[3]{x^{3}} \) and \( \sqrt[3]{x} \), because the rule of exponents states that when multiplying two bases with the same exponent, you can add the exponents. In other words, \( x^{3} * x = x^{4} \).
02

Simplifying the cube root of \( x^{3} \)

To simplify the \( \sqrt[3]{x^{3}} \), we find the cube root of \( x^{3} \), which is \( x \). This leaves us with the equation \( x * \sqrt[3]{x} \).
03

Final Expression

After simplifying, we get the simplified radical expression, \( x * \sqrt[3]{x} \), which is the final answer.

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Most popular questions from this chapter

Evaluate each exponential expression in Exercises 1鈥�22. $$ (-3)^{0} $$

Why must \(a\) and \(b\) represent non negative numbers when we write \(\sqrt{a} \cdot \sqrt{b}=\sqrt{a b ?}\) Is it necessary to use this restriction in the case of \(\sqrt[3]{a} \cdot \sqrt[3]{b}=\sqrt[3]{a b} ?\) Explain.

Rationalize the denominator. $$\frac{2}{\sqrt{10}}$$

Add or subtract as indicated. $$\frac{8}{x-2}+\frac{2}{x-3}$$

In Exercises 132鈥�135, determine whether each statement makes sense or does not make sense, and explain your reasoning. If \(5^{-2}\) is raised to the third power, the result is a number between 0 and 1
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