[tex]\huge\mathfrak\purple{Question:}[/tex]
[tex]\bold{If \: 3x−y = 12, what \: is \: the \: value \: of } \: \frac{8x}{2y} ?[/tex]
[tex]\huge\mathfrak\purple{Solution:}[/tex]
Since 2 and 8 are the both powers of 2, substitute 2³ for 8 in the numerator of:
[tex] \bold \purple{\frac{ {8}^{x} }{ {2}^{y} }} \: \bold{gives}[/tex]
[tex]{\boxed{\bold{\purple{ \frac{ {(2}^{3}) ^{x} }{ {2}^{y} } }}}} \: \bold{or \: }{\boxed{\bold{\purple{ \frac{ {2}^{3}x }{ {2}^{y} }}}}}[/tex]
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
[tex]{\boxed{\bold{\purple{ \frac{ {8}^{x} }{ {2}^{y} }}}}} = \green{ {2}^{12} }[/tex]
[tex]\huge\mathfrak\purple{Answer:}[/tex]
[tex]{\boxed{\bold{ \purple{ {2}^{12} }}}}[/tex]
[tex] \\ \\ [/tex]
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