Question

Which of the following is the correct radical form of this expression

Answer 1

The correct answer is A.

Step-by-step explanation

The given expression is

`( \frac{ {p}^(12) {q}^{ (3)/(2) } }{64} ) ^{ (5)/(6) }`

Recall that:

`{a}^{ (m)/(n) } = (\sqrt[n]{a} ) ^(m)`

For the given expression,

`m = 5`

`n = 6`

and

`a = \frac{ {p}^(12) {q}^{ (3)/(2) } }{64}`

We substitute all these values to obtain the radical form:

`( \frac{ {p}^(12) {q}^{ (3)/(2) } }{64} ) ^{ (5)/(6) } = ( \sqrt[6]{( \frac{ {p}^(12) {q}^{ (3)/(2) } }{64} ) })^(5)`

The correct choice is A.