(Solved) If 3x−y=12, what is the value of 8^x/2^y? A) 2^12 B) 4^4 C) 8^2 D) The value cannot be determined from the information given

 Question:

If 3x−y=12, what is the value of 8^x/2^y?

A) 2^12

B) 4^4

C) 8^2

D) The value cannot be determined from the information given.

Explanation:

8^x can be written as 2^3x because 8 = 2^3

So we need to find value of 2^3x/2^y

It is given that 3x-y=12

So 3x = 12+y

Substituting value of 3x in 2^3x/2^y

(2^3x) /(2^y) = (2^(12+y))/(2^y)

= 2^((12+y)-y)

= 2^12

Handwritten solution is provided below:

So answer is option (A) : 2^12