Question

2^2018+2^2017/2^2016+2^2017

Answer 1

SOLUTION

TO DETERMINE

$\displaystyle \sf{ \frac{ {2}^{2018} + {2}^{2017} }{ {2}^{2016} + {2}^{2017} } }$

EVALUATION

$\displaystyle \sf{ \frac{ {2}^{2018} + {2}^{2017} }{ {2}^{2016} + {2}^{2017} } }$

$\displaystyle \sf{ = \frac{ {2}^{2018} + {2}^{2017} }{ {2}^{2017} + {2}^{2016} } }$

$\displaystyle \sf{ = \frac{ {2}^{2017} \times (2 + 1) }{ {2}^{2016} \times ( 2+ 1) } }$

$\displaystyle \sf{ = \frac{ 3 \times {2}^{2017} }{3 \times {2}^{2016} } }$

$\displaystyle \sf{ = \frac{ {2}^{2017} }{ {2}^{2016} } }$

$\displaystyle \sf{ = {2}^{(2017 - 2016)} }$

$= {2}^{1}$

$= 2$

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