If `a and b` are different positive primes such that `(i)\ ((a^(-1)\ b^2)/(a^2b^(-4)))^7-:((a^3\ b^(-5))/(a^(-2)b^3))=a^x b^y ,` find `x\ a n d\ y` `(ii)\ (a+b)^(-1)\ (a^(-1)+b^(-1))=\ a^x b^y ,` find `x+y+2`

Explanation

Let's solve the given problems step by step.

### Problem (i):
We need to simplify the expression:
\[ \frac{(a^{-1} b^2)}{(a^2 b^{-4})}^7 \div \frac{(a^3 b^{-5})}{(a^{-2} b^3)} = a^x b^y \]

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