When adding and subtracting numbers in Scientific Notation, the powers of the base 10 must be the same exponent so that you have "like terms".
When multiplying and dividing numbers in Scientific Notation, you do not have to have the same power of the base 10. You can simply follow the exponent rules for multiplying and dividing with the like base 10.
True, coefficients follow the operations and exponents follow exponent rules when you are multiplying or dividing.
True, when multiplying and dividing you can just multiply the coefficients and multiply the exponents.