Answer:
x = 8 and y = -1.
Step-by-step explanation:
b^x / b^y = b^9
By the law of indices:-
b^(x - y) = b^9
therefore x - y = 9..........(1) . Also:
(b^x * b^2) / b^3y = b^13
b^(x + 2) / b^3y = b^13
b^(x + 2 - 3y) = b^13
Therefore x + 2 - 3y = 13.........(2)
From equation (1) y = x - 9 so substituting in equation 2:
x + 2 - 3(x - 9) = 13
x + 2 - 3x + 27 = 13
-2x = 13 - 2 - 27 = -16
x = 8
and from equation (1) y = 8-9 = -1
