Group theory/Exponent rules/Fact/Proof/Exercise

Let ${\displaystyle {}G}$ be a group, let ${\displaystyle {}g\in G}$ denote an element, and let ${\displaystyle {}m,n\in \mathbb {Z} }$ be integers. Show the following rules for the exponent.

1. We have ${\displaystyle {}g^{0}=e_{G}}$.
2. We have ${\displaystyle {}g^{m+n}=g^{m}g^{n}}$.