Question

solve it please
2^40 + 2^39 + 2^38
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2^41+ 2^40 _ 2^39

Answer 1

Let we consider that in denominator $\bold{2^{41}\: +\: 2^{40} \:-\:2^{39}}$.

$\bold{\underline{\underline{Solution\: \colon}}}$

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

$\bold{\implies\dfrac{2^{38}[2^{2}\: + \: 2 \: + \: 1]}{2^{39}[2^{2} \: + \: 2 \: - \: 1]}}$

$\bold{\implies \dfrac{ [4 \: + \: 2 \: + \: 1]}{(2)[4\: + \: 2 \: -\: 1]}}$

$\bold{\implies \dfrac{1[7]}{2[5]}}$

$\bold{\implies\dfrac{7}{10}}$

Decimal value $\bold{\boxed{0.7}}$

OR

Let we consider that in denominator $\bold{2^{41}\: +\: 2^{40} \:+\:2^{39}}$.

$\bold{\underline{\underline{Solution\: \colon}}}$

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

$\bold{\implies\dfrac{2^{38}[2^{2}\: + \: 2 \: + \: 1]}{2^{39}[2^{2} \: + \: 2 \: + \: 1]}}$

$\bold{\implies \dfrac{ [4 \: + \: 2 \: + \: 1]}{(2)[4\: + \: 2 \: +\: 1]}}$

$\bold{\implies \dfrac{1[7]}{2[7]}}$

$\bold{\implies\dfrac{1}{2}}$

Decimal value $\bold{\boxed{0.5}}$

These cases are due to your inappropriate symbol in a $\bold{denominator}$

$\bold{\large{Thanks}}$