Answer
$P=10^{19}$
Work Step by Step
We are asked to find the product:
$P=10^{1/10}\cdot 10^{2/10}\cdot 10^{3/10}\cdot 10^{4/10}... 10^{19/10}$
We simplify the powers:
$10^{(1+2+3+4+...+19)/10}$
We see that we have an arithmetic sequence with $a=1$ and $a_{19}=19$. We find the partial sum:
$S_{19}=\frac{19}{2}(1+19)=19*20/2=19*10=190$
Thus the product is:
$P=10^{190/10}=10^{19}$
