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