Answer
sometimes
Work Step by Step
If the given numbers are in scientific notation, then
$a$ and $b$ are numbers between 1 and 10 (less than 10).
(They have one nonzero digit before the decimal point).
If their product is greater than ten,
then $ab$ has two or more digits before the decimal point,
so $ab\times 10^{m+n}$ is NOT in scientific notation.
Example 1:
$(3.0\times 10^{2})(5.0\times 10^{3})=15.0\times 10^{5}$
(Each factor is in scientific notation; the product is not.
It needs to be manipulated...)
$15.0\times 10^{5}=1.5\times 10^{1}\times 10^{5}=1.5\times 10^{6}$
Example 2
$(3.0\times 10^{2})(2.0\times 10^{3})=6.0\times 10^{5}$,
which is in scientific notation.
So, the product CAN be in scientific notation.
Answer: sometimes.
