What does fractional power of number mean

Question

I have following query in my mind for many years.I know it sounds stupid and will delete if people don't like it.

I know that 2^3 means that multiply 2 three times,3^-2 means multiply (1/3) two times.What does 2^(0.22) means. multiply 2 how many times? i mean what is logic behind fractional power of integer?

Answer 1

a^(m/n) = n√(a^m)

It's n-th root of a^m

0.22 = 22/100
m=22
n=100

Answer 2

It is a root.

4 ^ 1/2 = sqrt(4)