$a)\sqrt{5^{-3}\cdot 5^5}=\sqrt{5^{-3+5}}=\sqrt{5^2}=5$

$b)\sqrt{6^7\cdot 6^{-3}}=\sqrt{6^{7+\left(-3\right)}}=\sqrt{6^4}=\sqrt{{\left(6^2\right)}^2}=\sqrt{{36}^2}=36$

$c)\sqrt{{12}^8\cdot {\left(\frac{1}{6}\right)}^8}=\sqrt{{\left(12\cdot \frac{1}{6}\right)}^8}=\sqrt{2^8}=\sqrt{{\left(2^4\right)}^2}=\sqrt{{16}^2}=16$

$d)\sqrt{{0,016}^2\cdot {0,1}^2}=\sqrt{{\left(0,016\cdot 0,1\right)}^2}=\sqrt{{0,0016}^2}=0,0016$