Explain how the rule that states that a^-n = 1/a^n is consistent with the rules that a^m/a^n = a^m-n and a^0 = 1 for a≠0.

[jyjvs2019]

Explain how the rule that states that a^-n = 1/aⁿ is consistent with the rules that a^m/aⁿ= a^m-n and a⁰ = 1 for a≠0.

 

[Dr.Peterson]

What would a^m/aⁿ= a^m-n look like if m=0?

 

[jyjvs2019]

a^-n

 

[Dr.Peterson]

And the left side?

Do you see what they are looking for?

 

[HallsofIvy]

Notice that n= 0 is the only number such that -n= n and b= 1 is the only number such that b= 1/b.