Evaluate: (\sqrt[5]{224})/(\sqrt[5]{7)}

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  3. Evaluate: (\sqrt[5]{224})/(\sqrt[5]{7)}

Expression: $\frac{\sqrt[5]{224}}{\sqrt[5]{7}}$

Apply radical rule $\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}},\quad a\ge0, b\ge0$

$=\sqrt[5]{\frac{224}{7}}$

Divide the numbers: $ \frac{224}{7}=32$

$=\sqrt[5]{32}$

Factor the number: $ 32=2^{5}$

$=\sqrt[5]{2^{5}}$

Apply radical rule $\sqrt[n]{a^n}=a,\quad a\ge0$

$=2$

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