Fix b> 1. (a) If m, n, p, q are integers, n>0, q>0, and r=m/n3Dplg, prove that \left(b^{m}\right)^{m / n}=\left(b^{p}\right)^{1 / 4} Hence it makes sense to define b=(b")". (b)

Prove that b**- b'b' if r and s are rational. (c) If x is real, define B(x) to be the set of all numbers b', where t is rational andt x Prove that b = sup B(r) when r is rational, Hence it makes sense to define b* =sup B(x)