order of operations with many level exponents 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?
Yes to both questions.

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