# Chapter 7 - Section 7.2 - Rational Exponents - 7.2 Exercises - Page 448: 49

$\dfrac{1}{\left( \sqrt[3]{3m^4+2k^2} \right)^{2}}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the laws of exponents and the definition of rational exponents to convert the given expression, $(3m^4+2k^2)^{-2/3} ,$ to radical form. $\bf{\text{Solution Details:}}$ Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{(3m^4+2k^2)^{2/3}} .\end{array} Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{\left( \sqrt[3]{3m^4+2k^2} \right)^{2}} .\end{array}

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