Simplify this expression to a common fraction: 11(12)^1+1(12)^2+1(12)^3

11(12)^1+1(12)^2+1(12)^3=121+41+81=114.

jmc

prealgebra intermediate

Problem

Simplify this expression to a common fraction:

\frac{1}{\frac{1}{( \frac{1}{2} ) ^{1}} + \frac{1}{( \frac{1}{2} ) ^{2}} + \frac{1}{( \frac{1}{2} ) ^{3}}}

Solution

\frac{1}{\frac{1}{( \frac{1}{2} ) ^{1}} + \frac{1}{( \frac{1}{2} ) ^{2}} + \frac{1}{( \frac{1}{2} ) ^{3}}} = \frac{1}{\frac{2}{1} + \frac{4}{1} + \frac{8}{1}} = \frac{1}{14}

Final answer

\frac{1}{14}