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?

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Answer 1 · 2016-01-02T07:36:40

#14(2^(x-2))#

First, write everything in terms of a power of #2#.

#((2^2)^(x+2)-2^(2x+1))/((2^3)^x((2^2)^(1-x))#

Simplify using the rule that #(x^a)^b=x^(ab)#.

#(2^(2x+4)-2^(2x+1))/(2^(3x)(2^(2-2x)))#

Simplify the denominator using the rule that #x^a(x^b)=x^(a+b)#.

#(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 #x^a/x^b=x^(a-b)#.

#2^(x+2)-2^(x-1)#

Factor out a #2^(x-2)# term.

#2^(x-2)(2^4-2)#

Simplify and write in #ab^(x-2)# form.

#14(2^(x-2))#