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Chapter 0: Problem 94

Convert the expressions to radical form. $$ \frac{3.1}{x^{-4 / 3}}-\frac{11}{7} x^{-1 / 7} $$

Short Answer

Expert verified
The short answer is: \[ 3.1\sqrt[3]{x^4} - \frac{11}{7}\sqrt[7]{x} \]

Step by step solution

01

Rewrite the expression

We start by rewriting the given expression: \[ \frac{3.1}{x^{-4/3}} - \frac{11}{7} x^{-1/7} \]
02

Convert negative exponents to positive exponents

Remember that a negative exponent in a fraction can be converted to a positive exponent by moving it from the denominator to the numerator or vice-versa: \[ 3.1x^{4/3} - \frac{11}{7} x^{1/7} \]
03

Convert rational exponents to radical notation

Now, we convert the rational exponents to radical notation. Recall that \(x^{a/b}\) can be written as \(\sqrt[b]{x^a}\): \[ 3.1\sqrt[3]{x^4} - \frac{11}{7}\sqrt[7]{x} \] This is the final converted expression in radical form.

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Most popular questions from this chapter

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(3\left(1+\frac{4}{100}\right)^{-3}\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(3.1 x^{3}-4 x^{-2}-\frac{60}{x^{2}-1}\)

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

Calculate each expression in Exencises giving the answer as \(a\) whole mumber or a fraction in lowest terms.\(\frac{12-(1-4)}{2(5-1) \cdot 2-1}\)

Find all possible real solutions of each equation \(2 x^{6}-x^{4}-2 x^{2}+1=0\)
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