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Exercises Equations and inequalities

Example 1 from Algebra and Trigonometry, 2.6 Other Types of Equations

Evaluating a Number Raised to a Rational Exponent

Evaluate $8^{\frac{2}{3}} .$

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.

Solution
Whether we take the root first or the power first depends on the number. It is easy to find the cube root of 8, so rewrite $8^{\frac{2}{3}}$ as ${(8^{\frac{1}{3}})}^{2} .$

$\begin{matrix} {(8^{\frac{1}{3}})}^{2} & = & {(2)}^{2} \\ = & 4 \end{matrix}$

Your turn

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

Evaluate $64^{- \frac{1}{3}} .$

How did it go?

PreviousFinding the Length of the Missing Side of a Right Triangle Next Solve the Equation Including a Variable Raised to a Rational Exponent

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 2.6, 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.