Determine if Force is Conservative or Not

nick227
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Homework Statement



For the following force, determine whether it is conservative or not.

Homework Equations



F=i(5abx^2+2ab^2y^5)+j(7abz^2+a^2b^3y)+k(18abz^3)

i, j, k being unit vectors and a and b are constants

The Attempt at a Solution



I found the curl to be: (-14abz)i-(10ab^2y^4)k. This means its non-conservative. I think this is correct, but some of my classmates got it to be conservative. If i am wrong, how do i go about this?
 
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the ans for your curl is correct.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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