How do you simplify #\frac { 2\cdot 2^ { 3} } { 2^ { 2} }#?

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Answer 1 · 2017-06-14T12:20:06

See a couple of solution processes below:

First, we can just expanded the terms with exponents:

#(2 * 2^3)/2^2 = (2 * 2 * 2* 2)/(2 * 2) = 16/4 = 4#

Another way is to use rules of exponents:

First, use these two rules of exponents to simplify the numerator:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#(2 * 2^3)/2^2 => (2^color(red)(1) * 2^color(blue)(3))/2^2 = > 2^(color(red)(1)+color(blue)(3))/2^2 => 2^4/2^2#

Next, use this rule of exponents to simplify the remaining terms:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#2^color(red)(4)/2^color(blue)(2) => 2^(color(red)(4)-color(blue)(2)) = 2^2 = 4#