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