(30^-1+60^-1+80^-1)^-1

(30^-1+60^-1+80^-1)^-1

$$\small{\text{ $ \begin{array}{rcl} &&\left( 30^{-1}+60^{-1}+80^{-1} \right)^{-1}\\\\ &=& \left( \dfrac{1}{30}+\dfrac{1}{60}+\dfrac{1}{80} \right)^{-1}\\\\ &=& \left( \dfrac{60\cdot 80+ 30\cdot 80+30\cdot 60}{30\cdot 60 \cdot 80} \right)^{-1}\\\\ &=& \dfrac{30\cdot 60 \cdot 80} {60\cdot 80+ 30\cdot 80+30\cdot 60}\\\\ &=& \dfrac{144000} {9000}\\\\ &=& 16 \end{array} $}}$$