When determining the product of two numbers written in scientific notation, you multiply the base numbers and add the exponents of the powers of ten.
For example, if you have \( (a \times 10^m) \) and \( (b \times 10^n) \), the product would be calculated as follows:
\[ (a \times b) \times 10^{(m+n)} \]
So, you multiply \( a \) and \( b \), and then add the exponents \( m \) and \( n \).