Question

If a and b are distinct primes such that `root3 (a^6b^-4)=a^xb^(2y),` find x and y.

Answer 1

Given `root3 (a^6b^-4)=a^xb^(2y)`

`rArr(a^6b^-4)^(1/3)=a^xb^(2y)`

`rArra^(6xx1/3)b^(-4xx1/3)=a^xb^(2y)`

`rArra^2b^(-4/3)=a^xb^(2y)`

⇒ x = 2 and y = -2/3