Properties of Exponents with Rationals

5.2.4 Properties of Exponents with Rationals

5.2.4 • Properties of Exponents with Rationals

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:

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