The product of [tex](a \cdot 10^n)(b \cdot 10^n)[/tex] is [tex]ab \cdot 10^{m+n}[/tex]. The answer is option C
Explanation
Product of [tex](a \cdot 10^n)(b \cdot 10^n)[/tex]
To find out the product , we apply exponential property
first we multiply 'a' and 'b', the product is ab
[tex](a \cdot b)(10^m \cdot 10^n)\\ab(10^m \cdot 10^n)\\[/tex]
Now use exponential property , when the base are same and the exponents are in multiplication then we add the powers
[tex]ab(10^m \cdot 10^n)\\\\ab(10^{m+n})\\ab \cdot 10^{m+n}[/tex]
Learn more : brainly.com/question/24420843
