Hello, I am confused regarding the following expression:
(-3^2)^(1/2). I know this can result in 9^(1/2) which = 3, but why wouldn’t it also yield (-3)^(2/2)=(-3)^1=-3? Wouldn’t both answers be valid? If not, why? Thanks!
(-3^2)^1/2 = sqrt(-3^2). We will apply PEMDAS for the Order of Operations. Since exponents precede multiplication, then sqrt(-3^2) = sqrt(-9), which is undefined.
The operation you defined where you bring the exponent to the power is not well-defined if the number inside the square root is negative. That rule applies if the number inside is positive or zero. I hope that clarifies.
If there were a parentheses, then ((-3)^2)^(1/2) = (9)^1/2 = 3, not -3. A square root that is already written on the page cannot be negative.
Hope that helps!
I see; the point about it not being well-defined for negative values is the piece I was missing. Thank you!