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\sqrt{\sqrt[3]{7}}:\sqrt[6]{7}=[(7^{\frac{1}{3}})^{\frac{1}{2}}:7^{\frac{1}{6}}=7^{\frac{1}{6}}:7^{\frac{1}{6}}=7^{\frac{1}{6}-\frac{1}{6}}=7^0=1
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5\cdot (\sqrt{\sqrt[3]{5^2}})^3=5\cdot (\sqrt{5^{\frac{2}{3}}})^3=5 \cdot \sqrt{5^{\frac{2}{3}\cdot 3}}=5\sqrt{5^2}=5\cdot 5=25