Question

The value of $\frac{2^{-14}+2^{-15}+2^{-16}+2^{-17}}{5}$ is how many times the value of $2^{-17}$ ?

• A. $\frac{3}{2}$
• B. $\frac{5}{2}$
• C. $3$
• D. $4$
• E. $5$

Answer 1

Answer: (C)

($3$)

Given $2^{-14}{+2}^{-15}{+2}^{-16}{+2}^{-17}5=\frac{2^{-14-3+3}{+2}^{-15-2+2}{+2}^{-16-1+1}{+2}^{-17}}{5}$
$=\frac{2^{-17}{2^3+2}^{-17}{2}^2{+2}^{-17}+2^1{\times 2}^{-17}}{5}$ [Since, $a^{m+n}=a^m\times a^n$]
$=2^{-17}\left(\frac{2^3{+2}^2+2^1+1}{5}\right)=2^{-17}\left(\frac{8+4+2+1}{5}\right)=2^{-17}\left(\frac{15}{5}\right)=2^{-17}\left(3\right)$

Hence, the given value $3$ times of $2^{-17}$