a)
\sqrt{15}*\sqrt{\frac{3}{5}}+\sqrt[3]{20}*\sqrt[3]{\frac{2}{5}}=\sqrt{\not15^3*\frac{3}{\not5^1}}+\sqrt[3]{\not20^4*\frac{2}{\not5^1}}=\sqrt9+\sqrt[3]8=3+2=5
b)
\sqrt{\sqrt[3]{216}+\sqrt[3]{32}+1}=\sqrt{6+\sqrt[3]{8*4}+1}=\sqrt{7+2\sqrt[3]4}=
=\sqrt{7+2^1*2^{\frac{2}{3}}}=\sqrt{7+2^{\frac{3+2}{3}}}=\sqrt{7+2^{\frac{5}{3}}}
c)
(\sqrt[3]{24}-2\sqrt[3]{81}+\sqrt[3]{192}):\sqrt[3]3=\frac{\sqrt[3]{8*3}-2\sqrt[3]{27*3}+\sqrt[3]{64*3}}{\sqrt[3]3}=
=\frac{2\sqrt[3]3-2*3\sqrt[3]3+4\sqrt[3]3}{\sqrt[3]3}=\frac{2\sqrt[3]3-6\sqrt[3]3+4\sqrt[3]3}{\sqrt[3]3}=\frac{0}{\sqrt[3]3}=0
d)
2^{-4}*(-\frac{1}{2})^{-3}-5^3*(-5)^{-2}+2^{-1}=(\frac{1}{2})^4*(-2)^3-5^3*(-\frac{1}{5})^2+\frac{1}{2}=
\frac{1}{\not16^2}*(-\not8^1)-\not125^5*\frac{1}{\not25^1}+\frac{1}{2}=-\frac{1}{2}-5+\frac{1}{2}=-5