Chapter 10 - Exponents and Radicals - Mid-Chapter Review - Mixed Review: 18

$\dfrac{a^{2}}{2}$

Work Step by Step

Using the properties of radicals, the expression, $\sqrt[5]{\dfrac{3a^{12}}{96a^2}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[5]{\dfrac{\cancel3a^{12-2}}{\cancel3\cdot32}} \\\\= \sqrt[5]{\dfrac{a^{10}}{32}} \\\\= \sqrt[5]{\left( \dfrac{a^{2}}{2} \right)^5} \\\\= \dfrac{a^{2}}{2} .\end{array} Note that the variable/s is/are assumed to be positive.

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