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I was wondering, what is the order of operations when it comes to multi level exponents. Couldn't find anything in google. Something like:

$$n^{n-1^{n-2^{\cdots^1}}}$$

In this case, if n equals 4, would it be correct to assume that 4^(3^(2^1)) is the correct order? And thus the answer is 262144?

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3 Answers

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Yes to both questions.

You should include parentheses around the differences, such as $$n^{(n-1)^{(n-2)^{\cdots^1}}}$$

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I will resurrect this thread since there seems to be confusion and the answers are contradictory.

The convention for stacked symbols in unambiguous- you work from the top down. Thus $a^{b^c}=a^{(b^c)}$.

When using carets there is no agreed convention and software systems and calculators may give different answers.

This a^b^c is ambiguous and should be avoided.

This question is addressed with references in

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No.

4^3^2 = 4^6 ; It does not equal 4^9. Multiple exponents evaluated from left to right. (4^3)^2. The power is 2*3=6. Because. First you get 4*4*4, and square that. It's alway true that you can multiply the exponents if there arent parenthesis grouping them in some way. 4^3^2^5 = 4^30

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