Which expressions are equivalent to $a^{\frac{p}{q}}$ ? Select all that apply.
A) $\sqrt[q]{a^{p}}$
B) $\sqrt[p]{a^{q}}$
C) $(\sqrt[q]{a})^{p}$
D) $\frac{a^{p}}{a^{q}}$
E) $a^{p - q}$
F) $\frac{1}{a^{\frac{q}{p}}}$

Answer

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Answer

F) $\frac{1}{(a^{\frac{q}{p}})^{p}} = a^{\frac{p}{q}}$

Steps

Step 1 ：A) $(\sqrt[q]{a^{p}})^{q} = a^{\frac{p}{q}}$

Step 2 ：C) $(\sqrt[q]{a})^{p} = a^{\frac{p}{q}}$

Step 3 ：F) $\frac{1}{(a^{\frac{q}{p}})^{p}} = a^{\frac{p}{q}}$