ANSWER
The correct answer is A.
EXPLANATION
The given expression is
[tex]( \frac{ {p}^{12} {q}^{ \frac{3}{2} } }{64} ) ^{ \frac{5}{6} } [/tex]
Recall that:
[tex] {a}^{ \frac{m}{n} } = (\sqrt[n]{a} ) ^{m} [/tex]
For the given expression,
[tex]m = 5[/tex]
[tex]n = 6[/tex]
and
[tex]a = \frac{ {p}^{12} {q}^{ \frac{3}{2} } }{64} [/tex]
We substitute all these values to obtain the radical form:
[tex]( \frac{ {p}^{12} {q}^{ \frac{3}{2} } }{64} ) ^{ \frac{5}{6} } = ( \sqrt[6]{( \frac{ {p}^{12} {q}^{ \frac{3}{2} } }{64} ) })^{5} [/tex]
The correct choice is A.
