Practice | Hashtable

Home > Practice > Arithmetic Aptitude > Surds and Indices > Miscellaneous

1. $\frac{2^{n + 4} - 2 (2^{n})}{2 (2^{n + 3})}$ when simplified is = ?

A. $2^{n + 1} - \frac{1}{8}$

B. -2⁽ⁿ⁺¹⁾

C. 1 - 2ⁿ

D. $\frac{7}{8}$

Solution:

\begin{aligned} \frac{2^{n + 4} - 2 (2^{n})}{2 (2^{n + 3})} \\ = \frac{2^{n + 4} - 2^{n + 1}}{2^{n + 4}} \\ = \frac{2^{n + 4}}{2^{n + 4}} - \frac{2^{n + 1}}{2^{n + 4}} \\ = 1 - 2^{(n + 1) - (n + 4)} \\ = 1 - 2^{- 3} \\ = 1 - \frac{1}{8} \\ = \frac{7}{8} \end{aligned}

You must login to add comments. Login now.