Answer:
A
Explanation:
Let's solve the equation to be written as y in terms of x by adding y to and subtracting 12 from both sides:
3x - y = 12
3x - 12 = y
Now, replace y in the other expression that we want to find ([tex]8^x/2^y[/tex]) with this expression 3x - 12:
[tex]8^x/2^y[/tex]
[tex]8^x/2^{3x-12}[/tex]
Now, we also know that 8 = 2³, so substitute 2³ for 8 in the expression:
[tex]8^x/2^{3x-12}[/tex]
[tex](2^3)^x/2^{3x-12}=2^{3x}/2^{3x-12}[/tex]
Remember that when dividing powers with the same base (in this case, the common base is 2), the result will be a single power whose exponent is the difference of the other two powers. Here, then we have:
[tex]2^{3x}/2^{3x-12}=2^{3x-(3x-12)}=2^{12}[/tex]
Thus, the answer is A.
