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

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Answer 1 · 2018-04-24T10:34:43

#(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#