Question

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

Answer 1

Answer:

A

Explanation:

Let's solve the equation to be written as y in terms of x by adding y to and subtracting 12 from both sides:

3x - y = 12

3x - 12 = y

Now, replace y in the other expression that we want to find ($8^x/2^y$) with this expression 3x - 12:

$8^x/2^y$

$8^x/2^{3x-12}$

Now, we also know that 8 = 2³, so substitute 2³ for 8 in the expression:

$8^x/2^{3x-12}$

$(2^3)^x/2^{3x-12}=2^{3x}/2^{3x-12}$

Remember that when dividing powers with the same base (in this case, the common base is 2), the result will be a single power whose exponent is the difference of the other two powers. Here, then we have:

$2^{3x}/2^{3x-12}=2^{3x-(3x-12)}=2^{12}$

Thus, the answer is A.

Answer 2

Answer:

A. 2¹²

Explanation:

8^x ÷ 2^y

2³^x ÷ 2^y

2^(3x) ÷ 2^y

2^(3x - y)

3x - y = 12

2^(3x - y)

2¹²