Can someone please explain why the exponent is 27 and not 9 (3x3)? Thanks.
I'll have to repeat what Bunuel already said:
(a^b)^c: Here, (a^b) should be executed first AND then the (result)^c should be executed.
If there are no brackets:
a^b^c: Then the precedence is from top to bottom. b^c should be executed first and then a^(result)
3^3^3=3^(result) i.e. 3^(27)
4^5^6: Execute 5^6 first. then find 4^(result obtained before)
(4^5)^6: Now, because of the bracket. 4^5 should be executed first and then result^6.
I really don't know who created this rule or what's the proof. I just accept is as a rule.
2+3*4-2=2+12-2=12. (It is another rule of precedence that multiplication should be done before addition or subtraction)
As I always say,
"A table is a table".