The given numbers are
5.78 x 10^5 and 8.04 x 10^-2
We would simplify the exponents by applying one of the laws of exponents which states that
a^b x a^c = a^(b + c)
By applying this law, the expression becomes
5.78 x 8.04 x 10^(5 + - 2)
46.4712 x 10^(5 - 2)
46.4712 x 10^3
The product in scientific notation is
46.4712 x 10^3