Answer:
[tex]2^{12}=4,096[/tex]
Step-by-step explanation:
You know that [tex]3x-y=12[/tex] and have to find
[tex]\dfrac{8^x}{2^y}[/tex]
Use the main properties of exponents:
1. [tex](a^m)^n=a^{m\cdot n}[/tex]
2. [tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]
Note that
[tex]8=2^3,[/tex]
then
[tex]7^x=(2^3)^x=2^{3\cdot x}=2^{3x}[/tex]
Now
[tex]\dfrac{8^x}{2^y}=\dfrac{2^{3x}}{2^y}=2^{3x-y}[/tex]
Since [tex]3x-y=12,[/tex] then [tex]2^{3x-y}=2^{12}=4,096[/tex]
