If 3x-y=123x−y=123, x, minus, y, equals, 12, what is the value of \dfrac{8^x}{2^y} 2 y 8 x start fraction, 8, start superscript, x, end superscript, divided by, 2, start superscript, y, end superscript, end fraction ?
Accepted Solution
A:
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]