If 3x - y = 12, what is the value of g^x/2^y?

To find the value of ( \frac{g^x}{2^y} ) given the equation ( 3x - y = 12 ), we first need to express ( y ) in terms of ( x ). We can rearrange the original equation as follows:

[

y = 3x - 12

]

Next, we will substitute this expression for ( y ) into ( \frac{g^x}{2^y} ):

[

\frac{g^x}{2^{3x - 12}}

]

This can be rewritten by separating the exponent:

[

\frac{g^x}{2^{3x} \cdot 2^{-12}} = \frac{g^x \cdot 2^{12}}{2^{3x}} = 2^{12} \cdot \frac{g^x}{2^{3x}}

]

This further simplifies into:

[

2^{12} \cdot \left(\frac{g}{2^3}\right)^x = 2^{12} \cdot \left(\frac{g}{8}\right)^x

]

Now, we need to