10 points. if 3x-y=12, what is the value of \frac{ {8}^(x) }{{2}^(y) } ? A {2}^(12) B {4}^(4) C {8}^(2) D the value cannot be determined from the information given.

Question

10 points.

if 3x-y=12, what is the value of

`\frac{ {8}^(x) }{{2}^(y) }`
?


A

`{2}^(12)`
B

`{4}^(4)`
C

`{8}^(2)`
D the value cannot be determined from the information given.

Answer 1

A, 2^12.

3x - y = 12 can also be written as 3x - 12 = y

The fraction is 8^x / 2^y,
Substitute y = 3x - 12 into fraction,
8^x / 2^[3x - 12]
= 8^x / [(2^3)^x × 2^(-12)]
= 8^x / [(2 × 2 × 2)^x × 2^(-12)]
= 8^x / [8^x × 2^(-12)]
{8^x can be factorised out of numerator and denominator of fraction}
= 1 / 2^(-12)
{When the denominator becomes numerator, the power sign is switched from - to +}
= 2^(12)

Hope this helps! :)