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Chapter 0: Problem 70

Simplify the radical expressions if possible. $$\sqrt[3]{x^{5}}$$

Short Answer

Expert verified
The simplified form of the expression \(\sqrt[3]{x^{5}}\) is \(x*\sqrt[3]{x^{2}}\).

Step by step solution

01

Identify the exponent inside the radical

The exponent of the variable \(x\) inside the radical is 5.
02

Simplify the expression

The cube root \(\sqrt[3]{x^{5}}\) means we are looking for a number that, when cubed (raised to the power 3), equals \(x^{5}\). We can write the 5 as a multiple of 3, which is the cube root, with some leftover. So, we write 5 as 3+2. Then the expression becomes \(\sqrt[3]{x^{3}} * \sqrt[3]{x^{2}}\). This simplifies to \(x*\sqrt[3]{x^{2}}\) since the cube root of \(x^3\) is \(x\).

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Most popular questions from this chapter

Explain how to factor \(x^{3}+1\)

Place the correct symbol, \(>\) or \(<,\) in the shaded area between the given numbers. Do not use a calculator. Then check your result with a calculator. $$\text { a. } 3^{\frac{1}{2}} \square 3^{\frac{1}{3}}$$ $$\text { b. } \sqrt{7}+\sqrt{18} \square \sqrt{7}+18$$

Evaluate each expression without using a calculator. $$32^{-\frac{4}{5}}$$

Factor completely. $$ x^{2 n}+6 x^{n}+8 $$

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