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10 points.

if 3x-y=12, what is the value of
[tex] \frac{ {8}^{x} }{{2}^{y} } [/tex]
?


A
[tex] {2}^{12} [/tex]
B
[tex] {4}^{4} [/tex]
C
[tex] {8}^{2} [/tex]
D the value cannot be determined from the information given.

Respuesta :

liz33312
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! :)

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