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Chapter 0: Problem 93

Convert the expressions to radical form. $$ 0.2 x^{-2 / 3}+\frac{3}{7 x^{-1 / 2}} $$

Short Answer

Expert verified
The expression in radical form is: \( \frac{0.2}{(\sqrt[3]{x})^2} + \frac{3\sqrt{x}}{7} \)

Step by step solution

01

Identify the rational exponents

The rational exponents in the given expression are -2/3 and -1/2. $$0.2x^{-\frac{2}{3}} + \frac{3}{7x^{-\frac{1}{2}}}$$
02

Convert the rational exponents to roots

In order to convert the rational exponents to roots, we can rewrite them as follows: $$ x^{-\frac{2}{3}}= (\sqrt[3]{x})^{-2} \quad \text{and} \quad x^{-\frac{1}{2}} = (\sqrt{x})^{-1} $$ Remember that \(- exponent\) means taking the reciprocal of the base.
03

Replace the exponents with roots in the expression

Now, we replace the rational exponents in the given expression with their corresponding roots that we found in Step 2: $$ 0.2(\sqrt[3]{x})^{-2} + \frac{3}{7(\sqrt{x})^{-1}} $$
04

Simplify the expression

Finally, we'll simplify the expression by dealing with the negative exponents (meaning taking the reciprocal), and present the result in radical form: $$ \frac{0.2}{(\sqrt[3]{x})^2} + \frac{3\sqrt{x}}{7} $$ The expression in radical form is as follows: $$ \frac{0.2}{(\sqrt[3]{x})^2} + \frac{3\sqrt{x}}{7} $$

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Most popular questions from this chapter

\((3 x+1)\left(2 x^{2}-x+1\right)\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(3\left(1-\left(-\frac{1}{2}\right)^{2}\right)^{2}+1\)

\(y^{4}+2 y^{2}-3\)

Calculate each expression in Exencises giving the answer as \(a\) whole mumber or a fraction in lowest terms.\(2 \cdot 4^{2}+1\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(2.1 x^{-3}-x^{-1}+\frac{x^{2}-3}{2}\)
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