# Math Help - x^{a+b}=x^ax^b

1. ## x^{a+b}=x^ax^b

G is a group and $x\in G$ and $a,b\in\mathbb{N}$.

Prove $x^{a+b}=x^ax^b$

I don't see how to show this. Multiplying by the inverse would just use the property I have to prove.

2. ## Re: x^{a+b}=x^ax^b

Could you just write this:

$x^{a+b}=\underbrace{x\cdot x\cdot...\cdot x}_{a+b\text{ times}}=\underbrace{x\cdot x\cdot...\cdot x}_{a\text{ times}}\cdot\underbrace{x\cdot x\cdot...\cdot x}_{b\text{ times}}=x^{a}x^{b},$

and claim you're done? I would definitely claim that there isn't much to show here. The proof can't be that complex.

3. ## Re: x^{a+b}=x^ax^b

More "rigorously", prove it by induction on a and b.