Question

where F is the magnitude of the gravitational attraction on either body, m1 and m2 are the masses of the bodies, r is the distance between them, and G is the gravitational constant. In SI units, the units of force are kg⋅m/s2, the units of mass are kg, and the units of distance are m. For this equation to have consistent units, the units of G must be which of the following?

Answer 1

                              Force  =  G  ·  m₁  ·  m₂   /   r²

In all SI units . . .

                        [ newton ]  =  [ G ] · [kg] · [kg] / [meter²]

But 'newton' is  kg-m / s²
So the formula says

                                  [ kg-m / s² ]  =  [ G ] · [kg] · [kg] / [meter²]

Divide each side
by  kg² :                    kg-m / s²-kg²  =  [ G ]  /  meter²

Multiply each side
by  meter² :              kg-m-m² / s²-kg²  =  G

Cancel 'kg' from
top and bottom:            m-m² / s²-kg  =  G

Clean it up:                    [ G ]  =  m³ / kg - s²      <==

Check:
Look up "Gravitational constant" on-line:
Gravitational constant =  6.67408 × 10-11 m³ kg⁻¹ s⁻²   <==          yay !