Question

TELL THE ANSWER FAST
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Answer 1

Answer:

$\rm{k=3}$

Step-by-step explanation:

$\rm{2^{1998}-2^{1997}-2^{1996}+2^{1995}=k \cdot 2^{1995}}$

$\to\rm{2^{1998}-2^{1997}-2^{1996}+2^{1995}=2^{1995} \cdot k}$

$\to\rm{2^{1995} \cdot k=2^{1998}-2^{1997}-2^{1996}+2^{1995}}$

$\to\rm{\displaystyle\frac{2^{1995} \cdot k}{2^{1995}}=\frac{2^{1998}-2^{1997}-2^{1996}+2^{1995}}{2^{1995}}}$

$\to\rm{\displaystyle k=\frac{2^{1995}\left(\frac{2^{1998}}{2^{1995}}-\frac{2^{1997}}{2^{1995}}-\frac{2^{1996}}{2^{1995}}+\frac{2^{1995}}{2^{1995}}\right)}{2^{1995}}}$

$\to\rm{\displaystyle k=\frac{2^{1995}\left(2^{1998-1995}-\left(2^{1997-1995}\right)-\left(2^{1996-1995}\right)\right.}{2^{1995}}}$

$\to\rm{\displaystyle k=\frac{2^{1995}\left(2^{3}-\left(2^{2}\right)-2+1\right)}{2^{1995}}}$

$\to\rm{\displaystyle k=\frac{2^{1995}(8-4-2+1)}{2^{1995}}}$

$\to\rm{\displaystyle k=\frac{2^{1995} \cdot 3}{2^{1995}}}$

$\to\rm{k=3}$

Answer 2

Answer:

3 is the correct answer

Step-by-step explanation:

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