Answer
294.307 u
Work Step by Step
To get the molecular mass, multiply the atomic mass of each element by the number of its atoms and add them together.
Molecular mass of aspartame ($C_{14}H_{18}N_{2}O_{5}$) = (14$\times$ atomic mass of carbon) + (18$\times$atomic mass of hydrogen) + (2$\times$atomic mass of nitrogen) + (5$\times$atomic mass of oxygen) = $(14\times12.011) + (18\times1.008) + (2\times14.007) + (5\times15.999)$ = 294.307 u