What is the Proof for the Jacobi Symbol Property (ii)?

[kingwinner]

This is a theorem about Jacobi symbols in my textbook:
Let n and m be ODD and positive. Then (a/nm)=(a/n)(a/m) and (ab/n)=(a/n)(b/n)
Moreover,
(i) If gcd(a,n)=1, then (a^2/n) = 1 = (a/n^2)
(ii) If gcd(ab,nm)=1, then (ab^2/nm^2)=(a/n)
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(i) is easy and follows from the definition, but how can we prove (ii)? My textbook stated the theorem without proof and just says the proofs are easy, but I have no idea why (ii) is true.

Any help is appreciated!

 

[robert Ihnot]

(a^2/n) = (a/n)(a/n). So what is it supposed to be?