Question

How do you write the expression `(5x)^-(5/4)` in radical form?

Answer 1

`1/((root4 (5x))^5)" or " 1/(root4 ((5x)^5)`

Explanation:

`(5x)^-(5/4)`

The negative index means we take the reciprocal to get:

`1/((5x)^(5/4)`

A fractional index shows a power and a root:

`x^(p/q) = (rootq x)^p or rootq(x^p)`

`1/((5x)^(5/4)) = 1/((root4 (5x))^5) or 1/(root4 ((5x)^5)`