Question

Simplify
Write your answer using only positive exponets.

Answer 1

Using the rule:

$x {}^{n} .x {}^{m} = x {}^{n + m}$

Similarly:

$x { }^{ \frac{1}{2} } .x {}^{ \frac{ - 1}{6} } .x {}^{ \frac{ - 5}{2} } = x {}^{ \frac{1}{2} - \frac{1}{6} - \frac{5}{2} }$

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

$x {}^{ \frac{3 - 1 - 15}{6} } =x {}^{ \frac{ - 13}{6} }$

To change our exponent to positive:

$x {}^{ \frac{ - 13}{6} } = \frac{1}{x {}^{ \frac{13}{6}}} = \frac{1}{ \sqrt[6]{x {}^{13} } } = \frac{1}{x \sqrt[6]{x} }$