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(3^4)^(a-b) . (5 . 3^2)^(a+b) = (5 . 3^3)^1/2
(3)^(4a-4b) . (5)^(a+b) . (3)^(2a+2b) = 5^1/2 . 3^3/2
(3)^(6a-2b) . 5^(a+b) = 5^1/2 . 3^3/2
#a + b = 1/2
2a + 2b = 1
2b = 1 - 2a
#6a - 2b = 3/2
12a - 4b = 3
12a - 2(1 - 2a) = 3
12a + 4a = 5
16a = 5
a = 5/16
2b = 1 - 2a
2b = 1 - 2(5/16)
2b = 1 - 5/8
2b = 3/8
b = 3/16