If z is a real number, then $\displaystyle \ {z^n}$ is defined recursively for non-negative integers

$\displaystyle \ n: {z^0}=1$

And, for $\displaystyle n\geq 0$

$\displaystyle \ {z^{n+1}} = z ({z^n}) $.

If z is a positive real number, and b a natural number, then we may define the positive bth root

$\displaystyle \ y= {z^{1/b}$ to be the positive real number y such that

$\displaystyle \ {y^b} = z$.

You may assume that a positive real number always has a positive bth root.

a) Given a positive real number z, is it possible for there to be two different positive bth roots of z? Justify your answer briefly.

Any help would be greatly appreciated