Respuesta :

loneguy

[tex]\text{Given that,}~3x-y = 12\\\\\\\dfrac{8^x}{2^y} =\dfrac{(2^3)^x}{2^y } = \dfrac{2^{3x}}{2^y} = 2^{3x-y} = 2^{12}[/tex]

DᴀʀᴋPᴀʀᴀᴅᴏx

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Let's solve ~

  • [tex] \sf3x - y = 12[/tex]

  • [tex] \sf3x = y + 12[/tex]

now, evaluate the value of given expression ~

  • [tex] \sf \dfrac{ {8}^{x} }{ {2}^{y} } [/tex]

  • [tex] \sf \dfrac{{(2 {}^{3} ) }^{x} }{ {2}^{y} } [/tex]

  • [tex] \sf \dfrac{2 {}^{3x} }{ {2}^{y} } [/tex]

Now, plug the value of 3x from the previous equation ~

  • [tex] \sf \dfrac{(2 ){}^{y + 12} }{ {2}^{y} }[/tex]

  • [tex] \sf2 {}^{ \ \cancel y + 12 - \cancel y} [/tex]

  • [tex] \sf{2}^{12} [/tex]

Therefore , the required expression is ~ 2¹²

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