Question

17. Efetue as potenciações:

$a)(\sqrt[5]{a})^{3} \\ b)(\sqrt[3]{m})^{2} \\ c)(\sqrt[6]{a^{2}})^{2}$
$d)(\sqrt[7]{x^{2}})^{3} \\ e)(3 \sqrt{a}^{2} \\ f)(2\sqrt[3]{a})^{2}$
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Answer 1

$(\sqrt[5]{a} ) {}^{3} = \sqrt[5]{ {a}^{3} } = {a}^{ \frac{3}{5} } \\ (\sqrt[3]{m}) {}^{2} = \sqrt[3]{ {m}^{2} } = {m}^{ \frac{2}{3} } \\ (\sqrt[6]{ {a}^{2} } ) {}^{2} = \sqrt[6]{ ({a}^{2})^{2} } = \sqrt[6]{ {a}^{4} } = a^{ \frac{4}{6} } = {a}^{ \frac{2}{3} } \\ ( \sqrt[7]{ {x}^{2} } ) {}^{3} = \sqrt[7]{( {x}^{2} ) {}^{3} } = \sqrt[7]{ {x}^{6} } = {x}^{ \frac{6}{7} } \\ 3 \sqrt{ {a}^{2} } = 9 {a}^{ \frac{2}{2} } = 9a \\( 2 \sqrt[3]{a} ) {}^{2} = {2}^{2} \times \sqrt[3]{ {a}^{2} } = 4 {a}^{ \frac{2}{3} }$