a)
\sqrt{\sqrt{81}}=\sqrt{9}=3
b)
\sqrt{ \sqrt[3]{7} } : \sqrt[6]{7}=\sqrt{(7)^{\frac{1}{3}}}: 7^{\frac{1}{6}}=7^{\frac{1}{3}*\frac{1}{2}}:7^ {\frac{1}{6} }=7^{\frac{1}{6}-\frac{1}{6}}=7^0=1
c)
5*(\sqrt{\sqrt[3]{5}})^3=5*( \sqrt{5^{\frac{1}{3} }})^3=5* \sqrt{5^{\frac{1}{3}*3}}=5\sqrt{5}
d)
\sqrt[3]{2}* (\sqrt[3]{(\sqrt{2})^2})^2 =2^{\frac{1}{3}} *(\sqrt[3]{2})^2 = 2^{\frac{1}{3}} * 2^{ \frac{2}{3} } = 2^{\frac{1}{3}+\frac{2}{3}} = 2