Simplify 16×2^n+1-4×2^n÷16×2^n+2-2×2^n+2?
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#(12(2^n) + 1)/(14(2^n) + 4)#
or
#1/2#
#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#
