How do you simplify #\frac { 2} { 2^ { - 1} + 2^ { - 2} }#?

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Answer 1 · 2017-11-14T12:47:00

#2/(2^(-1)+2^(-2))=8/3=2 2/3#

#2^(-1)=1/2#

#2^(-2)=1/(2^2)=1/4#

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

#2/(2^(-1)+2^(-2))=2/(3/4)=2xx4/3=8/3#

Answer 2 · 2017-11-14T15:37:34

#8/3#

another approach

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

multiply top and bottom by #" "2^2" "#in order to remove all teh negative powers

#2/(2^(-1)+2^(-2))xx2^2/2^2#

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

#(2^3)/(2^1+2^0)#

#=8/(2+1)=8/3#