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Exercises Roots and quadratic equations

Example 9.117 from Elementary Algebra, 9.8 Rational Exponents

Rational Exponents: example 9.117

Simplify: ⓐ ${(m^{3} n^{9})}^{\frac{1}{3}}$ ⓑ ${(p^{4} q^{8})}^{\frac{1}{4}}$ .

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
1. ⓐ
  $\begin{matrix} {(m^{3} n^{9})}^{\frac{1}{3}} \\ \begin{matrix} First we use the Product to a Power \\ Property. \end{matrix} & {(m^{3})}^{\frac{1}{3}} {(n^{9})}^{\frac{1}{3}} \\ \begin{matrix} To raise a power to a power, we multiply \\ the exponents. \end{matrix} & m n^{3} \end{matrix}$
2. ⓑ
  $\begin{matrix} {(p^{4} q^{8})}^{\frac{1}{4}} \\ \begin{matrix} First we use the Product to a Power \\ Property. \end{matrix} & {(p^{4})}^{\frac{1}{4}} {(q^{8})}^{\frac{1}{4}} \\ \begin{matrix} To raise a power to a power, we multiply \\ the exponents. \end{matrix} & p q^{2} \end{matrix}$

How did it go?

PreviousRational Exponents: example 9.116 Next Rational Exponents: example 9.118

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.