Question

How do you simplify `(4^(11/5)) (4^(-1/5))`?

Answer 1

`(4^(11/5))(4^(-1/5))=color(red)(16)`

Explanation:

Remember
[1]`color(white)("XXX")a^(-b)=1/(a^b)`
and
[2]`color(white)("XXX")(p^r)/(p^s)=p^(r-s)`

`(4^(11/5))(4^(-1/5))`

`color(white)("XXX")=(4^(11/5)) * (1/(4^5))`

`color(white)("XXX")=4^(11/5-1/5)`

`color(white)("XXX")=4^2`

`color(white)("XXX")=16`