#### Answer

$$8.95\times 10^{-12}$$

#### Work Step by Step

In scientific notation, the number of significant digits is the number of digits in the leading number between $1$ and $10$. The final answer should have the same number of significant digits as the least number of significant digits in any of the numbers involved in the multiplication:
$1.78\times 10^{-7}$ has $3$ significant digits
$5.03\times 10^{-5}$ has $3$ significant digits
Therefore, the final answer should be rounded to have $3$ significant digits.
Rearrange factors and multiply:
$$(1.78\times 10^{-7})(5.03\times 10^{-5})=(1.78\times 5.03)(10^{-7}\times 10^{-5})$$
$$=8.95\times 10^{-12}.$$