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

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The expression of a number raised to the power of another number raised to a power is evaluated from right to left. For example, in the case of 2^2^2, it is calculated as 2^(2^2), resulting in 16. This order of operations is crucial, as demonstrated by the example of 5^2^3, which equals 5^(2^3) = 5^8 = 390625, while evaluating it as (5^2)^3 yields a different result of 15625. Understanding this evaluation method is essential for accurate calculations in exponentiation.

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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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