# Chapter 7 - Section 7.2 - Rational Exponents - 7.2 Exercises: 51

$2^{6}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the definition of rational exponents to convert the given expression, $\sqrt{2^{12}} ,$ to exponential form. $\bf{\text{Solution Details:}}$ 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} \sqrt[2]{2^{12}} \\\\= 2^{\frac{12}{2}} \\\\= 2^{6} .\end{array}

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