suppose a^x/a^y = a^3 and a^x/a^3y = a^-5 solve for x and y

Question

part of quotient property lesson

Answer 1

a^x / a^y = a³

a^x-y = a³ So, x-y = 3

a^x / a^3y = a^-5

a^x-3y = a^-5 So, x-3y = -5

We have the system of equations x - y = 3 and x - 3y = -5

Subtract the equations to obtain 2y = 8.

Therefore, y = 4 and x = 7.