- #1
alianna
- 3
- 0
Let a be a nonzero number and m and n be integers. Prove the following equality. a^(m+n)=a^(m)a^(n)
Im not really sure what direction to go in. I am not sure if I need to show for n positive and negative separately or is there an easier way.
My attempt/ideas:
When n>0: a^(m)a^(n)= (a*a*...*a)(m times) *(a*a*a*a*...*a)(n times)
=a*a*...*a(m+n times)
=a^(m+n)
When n<0: a^(m)a^(n)=a^(m)=a...a(m times)/ a...a(n times)
Im not really sure what direction to go in. I am not sure if I need to show for n positive and negative separately or is there an easier way.
My attempt/ideas:
When n>0: a^(m)a^(n)= (a*a*...*a)(m times) *(a*a*a*a*...*a)(n times)
=a*a*...*a(m+n times)
=a^(m+n)
When n<0: a^(m)a^(n)=a^(m)=a...a(m times)/ a...a(n times)