Your friend says that the product of 2.1x10^7 and 3x10^-3 is 6.3x10^-4. What is the correct​ product? What mistake did your friend likely​ make?

The correct product of 2.1x10^7 and 3x10^-3 is:

(2.1 x 3) x (10^7 x 10^-3) = 6.3 x 10^4

Therefore, your friend made a mistake in adding the exponents instead of multiplying them. In the correct calculation, the exponents are multiplied rather than added.