Exponent confusion.

1. Feb 21, 2015

Benthal

My TI-89 calculator rearranged $$2^{2m+1}-1$$ to $$2\times 4^m - 1$$
I can't for life of me work out how it did it. Is anybody able to put me out of my misery?

Ben

2. Feb 21, 2015

Mentallic

It used two exponent rules:

$$\left(a^b\right)^c=a^{bc}$$

$$a^{b+c}=a^ba^c$$

So start by using the second to get rid of that pesky +1 in $2^{2m+1}$

3. Feb 21, 2015

Benthal

Oh god! Of course. I must not be feeling well.

Thanks.