Exponents and Variable Equalities

[RidiculousName]

I am not sure how to figure this out. Basically, I know X^N + X^N = 2X^N and that 2^N + 2^N = 2^N+1. So, since 2 * 2 = 4 why doesn't 2^N+1 = (2 * 2)^N = 4^N?

 

[Greg]

Why did you put the brackets there? Then you have to distribute N over both twos, which is not what you started out with.

 

[RidiculousName]

Why did you put the brackets there? Then you have to distribute N over both twos, which is not what you started out with.

Sorry, I am terrible with the syntax of math. How would I indicate that the 2s should be multiplied before the exponent is applied? (2(2))^N?

 

[Greg]

(2 * 2)$^\text{N}$

Is this part of a problem you're working on? If so, please post it and I'll be better equipped to help. :)

 

[topsquark]

2^N+1 = (2 * 2)^N = 4^N?

\(\displaystyle 2^{N + 1} = 2 \cdot 2^N \neq 4^N\)

-Dan

 

[RidiculousName]

(2 * 2)$^\text{N}$

Is this part of a problem you're working on? If so, please post it and I'll be better equipped to help. :)

I'm not really working on a problem. I'm just trying to figure out why it doesn't fit. I want to know the concepts behind the numbers here.

- - - Updated - - -

\(\displaystyle 2^{N + 1} = 2 \cdot 2^N \neq 4^N\)

-Dan

Thank you. I think I've got it. Basically in 2X^N the exponent is applied first. So that's why 2^N + 2^N = 2^N+1 but not 4^N