The Earth's mass is 6.0 × 10²⁴ kg, the Moon's is 7.35 × 10²² kg, and their centres are 3.84 × 10⁸ m…

Step 1. (a) In $F = \dfrac{GMm}{r^2}$, the top is $G \times 6.0 \times 10^{24}\ \text{kg} \times 7.35 \times 10^{22}\ \text{kg} = 2.94 \times 10^{37}\ \text{N m}^2$ and the bottom is $(3.84 \times 10^{8}\ \text{m})^2 = 1.47 \times 10^{17}\ \text{m}^2$, so $F = 1.99 \times 10^{20}\ \text{N}$.

Step 2. (b) Also $1.99 \times 10^{20}\ \text{N}$, towards the Moon: the two pulls are a third-law pair.

Step 3. (c) $a = \dfrac{1.99 \times 10^{20}\ \text{N}}{7.35 \times 10^{22}\ \text{kg}} = 0.00271\ \text{m/s}^2$.