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Exercises Roots and quadratic equations

Example 9.109 from Elementary Algebra, 9.8 Rational Exponents

Rational Exponents: example 9.109

Write with a rational exponent: ⓐ $\sqrt{y^{3}}$ ⓑ $\sqrt[3]{x^{2}}$ ⓒ $\sqrt[4]{z^{3}}$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
We want to use $a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$ to write each radical in the form $a^{\frac{m}{n}}$ .
1. ⓐ
2. ⓑ
3. ⓒ

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Write with a rational exponent: ⓐ $\sqrt{x^{5}}$ ⓑ $\sqrt[4]{z^{3}}$ ⓒ $\sqrt[5]{y^{2}}$ .

How did it go?

PreviousRational Exponents: example 9.108 Next Rational Exponents: example 9.110

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 9.8, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.