MHB Exponents and Variable Equalities

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The discussion centers on understanding the rules of exponents and variable equalities, specifically the expression 2N + 2N and its relation to 4N. It clarifies that 2N + 2N equals 2^(N + 1), not 4N, because the exponent applies to the base of 2 rather than the product of two twos. Participants discuss the correct notation for indicating multiplication before applying the exponent, with suggestions like (2 * 2)^N. Ultimately, the conclusion is that the exponent is applied first in the expression, which resolves the confusion. Understanding these concepts is crucial for correctly manipulating expressions involving exponents.
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I am not sure how to figure this out. Basically, I know XN + XN = 2XN and that 2N + 2N = 2N+1. So, since 2 * 2 = 4 why doesn't 2N+1 = (2 * 2)N = 4N?
 
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Why did you put the brackets there? Then you have to distribute N over both twos, which is not what you started out with.
 
greg1313 said:
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?
 
(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. :)
 
RidiculousName said:
2N+1 = (2 * 2)N = 4N?
[math]2^{N + 1} = 2 \cdot 2^N \neq 4^N[/math]

-Dan
 
greg1313 said:
(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.

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topsquark said:
[math]2^{N + 1} = 2 \cdot 2^N \neq 4^N[/math]

-Dan

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