How do you order two numbers written in scientific notation?

an * bn = (a*b) n am * an = a m+n

For which a and b are any positive real numbers and m and n are any real numbers.

Criteria:

Law 1: Same Index (exponent/power)

Example: 34 * 54 = (3*5) 4

Law 2: Same Base

Example: 42 * 44 = 4 (2+4) = 4 6