When are we suppose to rationalize the denominator?
like here, 1/ is that the final answer? how come we can't rationalize this denominator?
and other x^-1/5 and my teacher said the answer for this one is - 1/ how come? can't we rationalize the denominator?
this is so hard? can somebody ?

It is encouraged to rationalize the denomenator
you can rationalize the denomenator

one way is to convert to exponent
and remember your exponential rules
remember that
also,
and

so


so we want x^{4/4}, so 1/4+3/4=4/4
times the whole thing by to get

but, it looks alot nicer in the original form tho

the 2nd one, we multiply it by to get
but it looks nicer in original form tho

so you can ratinalize the denomenator but you don't always have to