Let G be a group with neutral element e Let g be an element

Let G be a group with neutral element e. Let g be an element of G. Let a and b be integers. Show that g^(a+b)= g^a . g^b

Solution

Given that G is a group with identity element e.

g is an element of G

Consider g^a.g^b = g*g*... a+b times

=g*g*... a times (g*g*...b times)

= (g^a)*(g^b)