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?
On
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
On
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 https://en.m.wikipedia.org/wiki/Order_of_operations
Yes to both questions.
You should include parentheses around the differences, such as $$n^{(n-1)^{(n-2)^{\cdots^1}}}$$