Exponents and Variable Equalities

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Discussion Overview

The discussion revolves around the properties of exponents and variable equalities, specifically examining the expressions involving exponents and their manipulation. Participants explore the implications of different notations and the rules governing exponentiation.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the equality 2N + 2N = 2N+1 and questions why 2N+1 does not equal 4N.
  • Another participant challenges the use of brackets in the expression, suggesting that it leads to incorrect distribution of the exponent.
  • A participant seeks clarification on how to indicate that the multiplication of the 2s should occur before applying the exponent.
  • One participant states that 2^{N + 1} = 2 \cdot 2^N and emphasizes that this does not equal 4^N, indicating a misunderstanding of exponent rules.
  • A later reply suggests that the exponent is applied first in the expression 2XN, which helps clarify the earlier confusion about the equality.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are differing interpretations of the expressions and the rules of exponentiation. Some participants clarify points while others express ongoing confusion.

Contextual Notes

There are limitations in the discussion regarding the notation used and the assumptions about the order of operations in exponentiation. The implications of different mathematical expressions remain unresolved.

RidiculousName
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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.

- - - Updated - - -

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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