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

1 Answer
Apr 24, 2018

(12(2^n) + 1)/(14(2^n) + 4)

or

1/2

Explanation:

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

color(blue)("First Answer:"
(16(2^n)+1-4(2^n))/(16(2^n)+2-2(2^n)+2)

From here you can collect like terms and simplify:
(12(2^n) + 1)/(14(2^n) + 4)

This is the most you can simplify this equation.

color(blue)"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

(14xx2^(n+1))/(14xx2^(n+2))

=(2xx2^n)/(2^2xx2^n)

=1/2