5.2.4 Properties of Exponents with Rationals

Algebra 15.2.4 Properties of Exponents with Rationals

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The activities you learned in a prior lesson taught you the properties of exponents. These same properties work with rational exponents.

Simplify each expression, and then check your answers.

${(x^{2})}^{\frac{1}{3}}$

Compare your answer:

$x^{\frac{2}{3}}$

$x^{\frac{2}{3}} \cdot x^{\frac{2}{3}}$

Compare your answer:

$x^{\frac{4}{3}}$

${(x^{- 3})}^{\frac{2}{5}}$

Compare your answer:

$x^{- \frac{6}{5}} = \frac{1}{x^{\frac{6}{5}}}$

${(x^{\frac{1}{3}})}^{- 1}$

Compare your answer:

$x^{- \frac{1}{3}} = \frac{1}{x^{\frac{1}{3}}}$

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
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- Book title: Algebra 1
- Publication date: Jun 4, 2025
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