Question

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

Answer 1

3x - y = 12
x = (12 + y) ÷ 3

8(12 + y)/3 ÷ 2y
= 4(12 + y)/3 × 1/y
=

Answer 2

One approach is to express

$\frac{ {8}^{x} }{ {2}^{y} }$

so that the numerator and denominator are expressed with the same base. Since 2 and 8 are both powers of 2, substituting 23 for 8 in the numerator of

8

$( \frac{ {2}^{3} }{ {2}^{y} })$

which can be rewritten

$\frac{ {2}^{3} x}{ {2}^{y} }$

Since the numerator and denominator of have a common base, this expression can be rewritten as 2(3x−y). In the question, it states that 3x−y=12, so one can substitute 12 for the exponent, 3x−y, which means that

$\frac{ {8}^{x} }{ {2}^{y} }$

=212