Answer
$10^{19}$
Work Step by Step
Applying the rule for multiplying powers with the same base,
$10^{a_{1}}\cdot 10^{a_{2}}\cdot....\cdot 10^{a_{n}}=10^{a_{1}+a_{2}+...+a_{n}}$
On the RHS, the exponent is the sum of the sequence
$0.1, 0.2, 0.3, ... , 1.9,$
which has a common differrence $d=0.1$,
so, it is arithmetic,
with first and last terms $a=0.1$ and $a_{19}=1.9.$
$S_{n}=n(\displaystyle \frac{a+a_{n}}{2})$
$S_{19}= 19(\displaystyle \frac{0.1+1.9}{2})=19$
Thus, the product equals $ 10^{19}$
