Question

If a and b are different positive primes such that

`((a^-1b^2)/(a^2b^-4))^7div((a^3b^-5)/(a^-2b^3))=a^xb^y,` find x and y.

Answer 1

`((a^-1b^2)/(a^2b^-4))^7div((a^3b^-5)/(a^-2b^3))=a^xb^y`

`rArr((a^-7b^14)/(a^14b^-28))div((a^3b^-5)/(a^-2b^3))=a^xb^y`

`rArr(a^(-7-14)b^(14+28))div(a^(3+2)b^(-5-3))=a^xb^y`

`rArr(a^-21b^42)div(a^5b^-8)=a^xb^y`

`rArra^(-21-5)b^(42+8)=a^xb^y`

`rArra^-26b^50=a^xb^y`

⇒ x = -26 and y = 50