What does it mean if I raise a power to the power etc?

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Discussion Overview

The discussion revolves around the evaluation of expressions involving exponents, specifically the interpretation of a number raised to the power of another exponent, such as 2 raised to the power of 2 raised to the power of 2. The scope includes mathematical reasoning and clarification of exponentiation order.

Discussion Character

  • Mathematical reasoning, Conceptual clarification

Main Points Raised

  • One participant states that the expression 2^2^2 is evaluated from right to left, leading to 2^(2^2) = 2^4 = 16.
  • Another participant notes that the order of evaluation does not affect the result in this specific case, as (2^2)^2 also equals 16.
  • A further example is provided where 5^2^3 can yield different results depending on the order of evaluation: 5^(2^3) = 5^8 = 390625 versus (5^2)^3 = 25^3 = 15625.

Areas of Agreement / Disagreement

Participants appear to agree on the evaluation order for the specific examples discussed, but there is an acknowledgment that different numbers can lead to different results, indicating a nuanced understanding of exponentiation.

Contextual Notes

The discussion does not resolve the broader implications of exponentiation order for all cases, and there may be assumptions about familiarity with exponent rules that are not explicitly stated.

Who May Find This Useful

This discussion may be of interest to individuals exploring mathematical concepts related to exponentiation and those seeking clarification on the order of operations in expressions involving powers.

jamesd2008
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What is the result of a number raised to the power of the number raised to a power.

I.e. 2^2^2?
 
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This expression is evaluated from right to left, as if parentheses were placed like so:
2^(2^2) = 2^4 = 16.

For this problem, the order isn't important, since (2^2)^2 = 4^2, also equals 16. For other problems with different numbers, thought, you can get different results.

For example, 5^2^3 = 5^(2^8) = 5^8 = 390625.

If you evaluate in the wrong order, you get (5^2)^3 = 25^3 = 15625.
 
Thats great thanks
 
Too soon to introduce him to "[URL Number[/URL]? :biggrin:
 
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