Monomials and Exponents?

[Dillinger4]

Can any one please work this out and tell me what you get.
(a^2m+3 / a^{m + 1})²

Im not quite sure how to break this down. It looks like simplification process should start out as (a⁵ / a²)² but then that would give us. a¹⁰ / a⁴ which judging by the answer a^{2m + 4} seems like the wrong way to go. Thanks.

[NotLKH]

a^2m+4?

Lets see, a^r*a^s = a^r+s

So, that makes a^2m+3 = a³*a^2m
and a^m+1 = a*a^m

so a³*a^2m/a*a^m = a²*a^m

which is a^m+2.

But now it needs to be squared, which is a^m+2*a^m+2 ==> a^2m+4.

I think.


-Lou

[DavidHooper]

Agreed.

[Dillinger4]

Thanks guys.