Simplify #(4^(x+2)-2^(2x+1))/(8^x (4^(1-x))# and express it in the form #ab^(x-2)#, where #a# and #b# are integers?
1 Answer
Jan 2, 2016
Explanation:
First, write everything in terms of a power of
#((2^2)^(x+2)-2^(2x+1))/((2^3)^x((2^2)^(1-x))#
Simplify using the rule that
#(2^(2x+4)-2^(2x+1))/(2^(3x)(2^(2-2x)))#
Simplify the denominator using the rule that
#(2^(2x+4)-2^(2x+1))/(2^(x+2))#
Split apart the fraction.
#(2^(2x+4))/(2^(x+2))-2^(2x+1)/2^(x+2)#
Simplify using the rule that
#2^(x+2)-2^(x-1)#
Factor out a
#2^(x-2)(2^4-2)#
Simplify and write in
#14(2^(x-2))#