Question

Choose the product.
(Sorry I closed it by accident)

Answer 1

Let's say we have something like:
\[a^{100}~ b^n~ a^2~ b^{n+1}\]
Now, the rule for exponents is that, when the terms are multiplied the powers for like bases get added up! When the terms are divided, the powers for like bases get subtracted.

What are the bases here? Well, they are a & b.
So how can you add the powers up? Simple addition!
\[a^{100}~ b^n~ a^2~ b^{n+1} = a^{100 + 2} ~b^{n + (n+1)} = a^{102}~b^{2n+1}\]
Can you try solving your question now? :)

Answer 2

Wait, so just add like the b's together and their powers?

Answer 3

Yes, let us take another case.

\(a^m ~b^n~ a^2~ b^3 = ~?\)

What is the answer? ;-)

Answer 4

a^m+2 b^n+3 ?

Answer 5

Excellent! :)

Try this now: \[\frac{a^m ~ b^n}{a^2 ~ b^3}\]

Answer 6

what am I doing with that...?

Answer 7

Can you try solving that?
It is the same thing, well, here we are just dividing. I think this ought to be your next topic.

To divide like terms with exponents on them, we simply subtract the exponents (or powers).

If you had something like: \[\frac{a^3}{a^2} = a^{3-2} = a\]
Similarily, \[\frac{a^m}{a^n} = a^{m-n}\]
Also, \[\frac{a^m~b^p~a^r}{a^n~b^q} = a^{m+r-n}~ b^{p-q}\]

Are you getting the rule?

Can you try answering the question you posted using these rules? :)