Hi,
On the quant mountain group 4, “Operation on Roots 1” row it says:
I have two questions regarding this:
-
It says “if a>0”, my question is, why does “a” have to be greater than 0 for the second expression to be valid:
Doesn’t this expression apply to any value of “a” whether it is positive, negative or 0?
-
Secondly, I wanted to know if there is an order of operation for fractional exponents?
For example, is a^(2/2) equal to:
Option 1:
OR Option 2:
In other words, do we do the exponent first and then the root or the root first and then the exponent?
This seems to determine if the result will be an absolute value or not, and hence, it seems important to know.
Thank you in advance for you response!
hm yea Idk why a > 0 for the second expression it should be all real numbers
for your second question that really depends on if a >= 0
you can’t plug in a negative number for a in option 1
Hi, thank you for your response!
for your second question that really depends on if a >= 0
Sure, let’s presume that a>=0 then which expression is correct?
Then you can use any operation you’d like they are essentially the same in that case. In your example a^2/2 you can just simplify first and get a^1 = a.
and I guess for the order of operations if we follow pemdas you can see that raising x^2 is on the same order as x^1/2 they are both exponents.
The bug on \sqrt{a^2} = |a| has been fixed - this is valid for all real numbers a, not just positive.
Usually, you’d want to restrict a > 0 to “combat” said ambiguity because that’s the “condition” required for your exponent laws to hold. Once you do that then both cases reconcile with each other.
