## Precalculus: Mathematics for Calculus, 7th Edition

$10^{19}$
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 $10^{19}$