Question

Simplify: $\frac{16\times 2^{n+1}-4\times 2^n}{16\times 2^{n+2}-2\times 2^{n+2}}$.

• A. $\frac{3}{2}$
• B. $\frac{5}{2}$
• C. $-\frac{1}{2}$
• D. $\frac{1}{2}$

Answer 1

The correct option is D $\frac{1}{2}$

$\frac{16\times 2^{n+1}-4\times 2^n}{16\times 2^{n+2}-2\times 2^{n+2}}$

$=\frac{16\times 2\times 2^n-4\times 2^{2n}}{16\times 2^2\times 2^n-2\times 2^2\times 2^n}$ $(as{a}^{m+n}=a^m-a^n)$

$=\frac{2^n(16\times 2-4)}{2^n(16\times 2^2-2\times 2^2)}$

$=\frac{32-4}{16\times 4-2\times 4}=\frac{28}{56}=\frac{1}{2}$