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))