If a and b are nonzero integers and a^{3b} = a^{b-6}, what is the value of b^{a}?
(A) a^3 = 8
(B) a^2 = 4
(A) a^3 = 8
(B) a^2 = 4
[Reveal] Spoiler:
I understand that (A) is sufficient. But if I simplify the given equation algebraically -
a^3b = a^b6
a^3b/ a^b6 = 1
a^(3b-b+6) = 1
a^(2b+6) = 1
(a^2)^b * a^6 = 1
(a^2)^b * (a^2)^3 = 1
This would make (B) sufficient, wouldn't it? Am I missing something in my simplification? Appreciate any pointers. Thanks.
a^3b = a^b6
a^3b/ a^b6 = 1
a^(3b-b+6) = 1
a^(2b+6) = 1
(a^2)^b * a^6 = 1
(a^2)^b * (a^2)^3 = 1
This would make (B) sufficient, wouldn't it? Am I missing something in my simplification? Appreciate any pointers. Thanks.