$a)\sqrt{81\cdot 144}=\sqrt{9^2\cdot {12}^2}=9\cdot 12=108$

$\sqrt{100\cdot 169}=\sqrt{{10}^2\cdot {13}^2}=10\cdot 13=130$

$\sqrt[3]{8\cdot 125}=\sqrt[3]{2^3\cdot 5^3}=2\cdot 5$

$\sqrt[3]{27\cdot 216}=\sqrt[3]{3^3\cdot 6^3}=3\cdot 6=18$

$\sqrt[3]{64\cdot 0,001}=\sqrt[3]{4^3\cdot {\left(0,1\right)}^3}=4\cdot 0,1=0,4$

$b)\sqrt{0,04\cdot 0,81}=\sqrt{{\left(0,2\right)}^2\cdot {\left(0,9\right)}^2}=0,2\cdot 0,9=0,18$

$\sqrt[3]{-0,008\cdot 64}=\sqrt[3]{{\left(-0,2\right)}^3\cdot 4^3}=-0,2\cdot 4=-0,8$

$\sqrt[3]{0,027\cdot 8}=\sqrt[3]{{\left(0,3\right)}^3\cdot 2^3}=0,3\cdot 2=0,6$

$\sqrt{0,01\cdot 144}=\sqrt{{\left(0,1\right)}^2\cdot {12}^2}=0,1\cdot 12$

$\sqrt[3]{-125\cdot 1}=\sqrt[3]{{\left(-5\right)}^3\cdot 1^3}=-5\cdot 1=-5$