# Simplify 16×2^n+1-4×2^n÷16×2^n+2-2×2^n+2?

Apr 24, 2018

$\frac{12 \left({2}^{n}\right) + 1}{14 \left({2}^{n}\right) + 4}$

or

$\frac{1}{2}$

#### Explanation:

color(blue)("there are two solutions based on the way to read the question "

color(blue)("First Answer:"
$\frac{16 \left({2}^{n}\right) + 1 - 4 \left({2}^{n}\right)}{16 \left({2}^{n}\right) + 2 - 2 \left({2}^{n}\right) + 2}$

From here you can collect like terms and simplify:
$\frac{12 \left({2}^{n}\right) + 1}{14 \left({2}^{n}\right) + 4}$

This is the most you can simplify this equation.

$\textcolor{b l u e}{\text{Second Answer:}}$

(16xx2^(n+1)-4xx2^n)/(16xx2^(n+2)-2xx2^(n+2)

Take ${2}^{n + 2}$ as a common factor from the denominator

(16xx2^(n+1)-2xx2xx2^n)/((16-2)xx2^(n+2)

color(green)(a^bxxa^c=a^(b+c)

(16xx2^(n+1)-2xx2^(n+1))/((16-2)xx2^(n+2)

Simplify

$\frac{14 \times {2}^{n + 1}}{14 \times {2}^{n + 2}}$

$= \frac{2 \times {2}^{n}}{{2}^{2} \times {2}^{n}}$

$= \frac{1}{2}$