Solving a system of equations with an exponential

Question

I've been trying to solve this problem for a while now and can't seem to figure it out.

If $3x - y = 12$, what is the value of $\frac{8^x}{2^y}$?

The answer should be $2^{12}$ but I'm not sure how to get there. Here's what I begin with.

$$y= 3x - 12$$ $$\frac{8^x}{2^{3x-12}}$$

And then I get stuck. I don't know how to simplify the equation when both the base and the exponents are different. Any help would be much appreciated.

Answer 1

Always try to get your exponentials with the same base. Note that we have

$$8=2^3$$

Which means

$$\frac{8^x}{2^{3x-12}}=\frac{2^{3x}}{2^{3x-12}}$$

Can you take it from here?

Answer 2

$8=2^3$ S0, the numerator is $2^{3x}$

$2^{3x} \over 2^{3x-12}$=$2^{12}$