I have read Loius' response, but before I comment further, it would be very helpful to know more details about the reasoning you used to get -1^(1/2) equal to -1. After that, I think I can help you sort out why -1 is incorrect. "

"Aren't taking a number to the 1/2 power and taking the square root of that number the same? " is true but I am not sure how that lead you to -1. Thanks.

I would like to know if there is any method to make an estimation on how big it is a number, in terms of orders of magnitude of n! when n is a big number.

(x^2) (2-x)^2 = 1 + 2(2-x)^2 I asked this problem on this page a few months ago, but didn’t get any satisfactory answer. I think there is a trick solution to it

-1^(1/2) is not equal to sqrt(-1).

When evaluating -1^(1/2), the exponent is only being applied to the 1 and the negative is added later.

When evaluating sqrt(-1), the square root is being applied to -1.

(-1)^(1/2) = sqrt(-1) is a true statement.

I have read Loius' response, but before I comment further, it would be very helpful to know more details about the reasoning you used to get -1^(1/2) equal to -1. After that, I think I can help you sort out

why-1 is incorrect. ""Aren't taking a number to the 1/2 power and taking the square root of that number the same?" is true but I am not sure how that lead you to -1. Thanks.The problem is not in the exponent, rather the base.

-1^(1/2)=-sqrt(1)=-(1^(1/2))=-1

sqrt(-1)=(-1)^(1/2)=i

Notice the difference in the base.

Also recall order of operations: Exponents are evaluated before multiplying by the negative (ie. -1).

@Louis Romao

This is, of course, perfectly correct. To the original poster - always remember 3x^2 is not the same as (3x)^2