The answer is 9, but I have no idea how to solve this, please help!
If a > 1 in the equation a^x / a^y = a^-6 and a^x * a^y = a^12, what is the value of y?
ok remember your rules of exponents?
a^x / a^y = a^-6 is the same as a^(x-y) = a^-6 and a^x * a^y = a^12 is the same as a^(x+y)=a^12
So x-y=-6 and x+y=12 solve it using elimination substitution whatever and you will get x=3 and y=9
Incase it isn’t clear
x-y=-6
x+y=12
The y cancels out and you get 2x=6 and x=3, substitute into either of the top equations and you get y=9
Or:
a^x / a^y = a^-6 (1)
a^x * a^y = a^12 (2)
Divide left hand side and right hand side of equation (2) respectively by LHS and RHS of equation (1),
a^(2y) = a^18
y = 9.
thank you so much!
Any time!
PS. As @Brajia suggested, brush up on [Rules of Exponents](Laws of Exponents).