Question

Evaluate 2^40+2^39+2^38/2^41+2^40-2^39

Answer 1

$\dfrac{2^{40}+2^{39}+2^{38}}{2^{41}+2^{40}-2^{39}}$

$= \dfrac{2^{38}[2^{2}+2^{1}+2^{0}]}{2^{39}[2^2 +2^{1}-2^{0}]}$

$= \dfrac{2^{38}[4+2 +1 ] }{2^{39}[4 +2 - 1]}$

$= \dfrac{1[7] }{2[5]}$

$= \dfrac{7}{10}$

Answer 2

$\frac{ {2}^{40} + {2}^{39} + {2}^{38} }{ {2}^{41} + {2}^{40} - {2}^{39} } \\ \\ = \frac{ {2}^{38} ( {2}^{2} + 2 + 1 )}{ {2}^{39}( {2}^{2} + 2 - 1 } \\ \\ = \frac{4 + 2 + 1}{ {2}^{39 - 38}(4 + 2 - 1) } \\ \\ = \frac{7}{2 \times 5} \\ \\ = \frac{7}{10} \\ \\ = 0.7$