Three of the most important fundamental constants in physics are:

Newton’s constant ("Big G"),G= 6.67×10−11 m 3/kg s2; the speed of light, c= 3.00×108 m/s; and Planck’s constant, h= 6.63×10−34 kg m2/s.

Use dimensional analysis to combine these constants to construct an expression (a single term) for a quantity with dimensions of (a) time, (b) mass, and (c) length and evaluate each numerically. Note: Make sure to solve for the form of the expressions to demonstrate uniqueness and not merely verify that an expression from some method (like guess and check) works.