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 diving with the base 10.
For multiplying numbers in scientific notation, you multiply the coefficients and add the exponents of the base 10.
For example:
(3 x 10^5) x (2 x 10^2) = 6 x 10^(5+2) = 6 x 10^7
For dividing numbers in scientific notation, you divide the coefficients and subtract the exponents of the base 10.
For example:
(4 x 10^6) / (2 x 10^3) = 2 x 10^(6-3) = 2 x 10^3
Remember to always simplify your answer by getting the coefficient into scientific notation if necessary.