How TI-89 Calculator Rearranged Exponent Confusion - Ben

[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?

Thank you in advance!

Ben

 

[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 $2^{2m+1}$

 

[Benthal]

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

Thanks.