\(165-\left\{3\left[416-\left(5^2.3-71\right)^2\right]+10^2\right\}:20\)
\(=165-\left\{3\left[416-\left(25.3-71\right)^2\right]+100\right\}:20\)
\(=165-\left\{3\left[416-\left(4\right)^2\right]+100\right\}:20\)
\(=165-\left\{3\left[416-16\right]+100\right\}:20\)
\(=165-\left\{3.400+100\right\}:2=165-1300:20\)
\(=165-65=100\)