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Exercises Expressions, exponents and radicals

Example 12 from Algebra and Trigonometry, 1.3 Radicals and Rational Exponents

Writing Radicals as Rational Exponents

Write $\frac{4}{\sqrt[7]{a^{2}}}$ using a rational exponent.

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.

Solution
The power is 2 and the root is 7, so the rational exponent will be $\frac{2}{7} .$ We get $\frac{4}{a^{\frac{2}{7}}} .$ Using properties of exponents, we get $\frac{4}{\sqrt[7]{a^{2}}} = 4 a^{\frac{−2}{7}} .$

Your turn

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

Write $x \sqrt{{(5 y)}^{9}}$ using a rational exponent.

How did it go?

PreviousWriting Rational Exponents as Radicals Next Simplifying Rational Exponents

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 1.3, 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.