Question

Simplify
Write your answer using only positive exponets.

Answer 1

Using the rule:

`x {}^(n) .x {}^(m) = x {}^(n + m)`

Similarly:

`x { }^{ (1)/(2) } .x {}^{ ( - 1)/(6) } .x {}^{ ( - 5)/(2) } = x {}^{ (1)/(2) - (1)/(6) - (5)/(2) }`

We have to achieve a common denominator which is 6 here:

`x {}^{ (3 - 1 - 15)/(6) } =x {}^{ ( - 13)/(6) }`

To change our exponent to positive:

`x {}^{ ( - 13)/(6) } = \frac{1}{x {}^{ (13)/(6)}} = \frac{1}{ \sqrt[6]{x {}^(13) } } = \frac{1}{x \sqrt[6]{x} }`