Originally Posted by

**AliceFisher** Thanks for the help Craig, answering the first has let me answer most of the other questions but I still seem to be drawing a blank on the second.

So the question is:

$\displaystyle \sqrt[3]{a^4b^5}*\sqrt[3]b/a$

which could be written as:

$\displaystyle (a^4)^\frac{1}{3}(b^5)^\frac{1}{3}*b^\frac{1}{3}*a ^{-1})$

So

$\displaystyle (a^\frac{4}{3})*(b^\frac{5}{3})*(b^\frac{1}{3})*(a ^{-1})$

To get the above answer would mean that:

Using the multiplication rule on the powers of a and b respectively gives:

$\displaystyle (a^\frac{1}{3})*(b^\frac{6}{3})$

or

$\displaystyle (a^\frac{1}{3})*(b^2)$

However the answer in the book is:

$\displaystyle (a^\frac{-1}{4})(b^2)$

To get this answer the first simplification would need to be:

$\displaystyle (a^\frac{3}{4})(b^\frac{5}{3})*b^\frac{1}{3}*a^{-1})$

but I have no idea how you would get this result for the first a...