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.
In multiplication, the exponents of the base 10 are added together. For example, when multiplying (3 x 10^4) by (4 x 10^3), the exponents are added: 4 + 3 = 7. So the result is 12 x 10^7.
Similarly, in division, the exponents of the base 10 are subtracted. For example, when dividing (3 x 10^4) by (4 x 10^3), the exponents are subtracted: 4 - 3 = 1. So the result is 0.75 x 10^1 or 7.5 x 10^0.
So, in multiplication and division, the powers of the base 10 do not necessarily have to be the same exponent, but they are manipulated according to the rules of exponents.