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

Question

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

A) 2¹²

B) 4⁴

C) 8²

D) The value cannot be determined

Answer 1

Answer 2

1. First, let's try to find a common denominator for both halves of the fraction. In this case, 8 can be rewritten as 2³
2. Next, simplify using the power of a power property where (xⁿ)^m = x^n*m so we get (2³)^x = 2^3x. Altogether we now have (2^3x / 2^y)
3. Using the quotient of powers property, which states that (xⁿ / x^m) = x^n-m, we can rewrite the second equation as 2^3x-y.
4. We were given in the prompt that 3x-y = 12 so the final answer is A) 2¹².

Answer 3

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

A) 2¹²

B) 4⁴

C) 8²

D) The value cannot be determined

A. First we can solve the first equation for y:

3x-12=y

B. We can now plug in 3x-12=y into our second value:

(8^x)/(2^(3x-12))

C. We can now simplify this expression by factoring out the 3 in the denominator:

(8^x)/(2^3(x-4))

D. We can further simplify this by converting 2^3 into 8:

(8^x)/(8^(x-4)

E. Now we can use the quotient of powers property which gives us:

(8^(x-x+4))

F. With some final simplification, we get:

(8^4) which is equivalent to 2^12

So the answer is A) 2^12