If the distance of the moon to earth were 0.25 times its current distance, the moon would exert a gravitational force on the earth how many times larger than its current value?

The new force will be 16 times the current value.

Explanation:

Lets say,

Mass of the Earth = M

Mass of the Moon = m

Distance between Earth and Moon = r

Gravitational force between the two = F

The gravitational force between the two is given as,

where, G = Gravitational constant

The new distance = 0.25r

So, the gravitational force (F') will be,

F' = 16 F

The new force will be 16 times the current value.

they start with the same

see earlier answer