solve this question---**Question Stem:** If 3x - y = 12, what is the value of (8^x)/(2^y)? **Options:** A) 2^12 B) 4^4 C) 8^2 D) The value cannot be determined from the information given.

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We have an algebraic problem. Given that 3x minus y equals 12, we need to find the value of 8 to the power x divided by 2 to the power y. Let's start by analyzing what we have and what we need to find. The key insight is to express both terms using the same base. Since 8 equals 2 to the power of 3, we can rewrite our expression. The original expression 8 to the power x divided by 2 to the power y becomes 2 to the power 3, all raised to the power x, divided by 2 to the power y. Now we apply exponent rules to simplify. First, we use the power of a power rule: 2 to the 3rd power, all raised to the x power, equals 2 to the 3x power. Next, we apply the division rule for exponents: 2 to the 3x power divided by 2 to the y power equals 2 to the power of 3x minus y. Now we use the given information. We simplified our expression to 2 to the power of 3x minus y. From the given equation, we know that 3x minus y equals 12. Therefore, we can substitute 12 for the exponent 3x minus y, giving us 2 to the power of 12 as our final answer. We have successfully solved the problem. The value of 8 to the power x divided by 2 to the power y equals 2 to the power 12. This corresponds to option A in the multiple choice answers. The solution required expressing both terms with a common base, applying exponent rules, and substituting the given constraint equation.