Exercise
8
[20T]Prerequisites:[202].Given \(๐ผโ 0\) in a field, define that \(๐ผ^ 0=1\) and let \(๐ผ^{-n}\) be the multiplicative inverse of \(๐ผ^ n\) when \(nโฅ 1\) natural. (Use [202]). For \(n,mโโค\) show that
\[ ๐ผ^{n}๐ผ^ m=๐ผ^{n+m}\quad ,\quad (๐ผ^ h)^ k=๐ผ^{(hk)}\quad ; \]
if the field is ordered and \(๐ผ{\gt}1\) show that \(nโฆ ๐ผ^ n\) is strictly monotonic increasing.