a: \(\sqrt{x^2\cdot x^{-2}\cdot\sqrt[3]{x}}\)
\(=\sqrt{x^{2-2}\cdot x^{\dfrac{1}{3}}}=\sqrt{x^{\dfrac{1}{3}}}=x^{\dfrac{1}{3}\cdot\dfrac{1}{2}}=x^{\dfrac{1}{6}}\)
b: \(\sqrt{x^2y^4:\sqrt[3]{xy}}\)
\(=\sqrt{x^2y^4:x^{\dfrac{1}{3}}y^{\dfrac{1}{3}}}\)
\(=\sqrt{x^{\dfrac{5}{3}}y^{\dfrac{11}{3}}}\)
\(=x^{\dfrac{5}{3}\cdot\dfrac{1}{2}}\cdot y^{\dfrac{11}{3}\cdot\dfrac{1}{2}}=x^{\dfrac{5}{6}}y^{\dfrac{11}{6}}\)
c: \(\dfrac{x^3\cdot x^{-\dfrac{1}{2}}\cdot x^5\cdot y}{y^3\cdot y^2\cdot x^3\cdot x^{-1}}=\dfrac{x^{3+5-\dfrac{1}{2}}\cdot y}{x^{3-1}\cdot y^5}=\dfrac{x^{\dfrac{15}{2}}}{x^2}\cdot\dfrac{1}{y^4}=\dfrac{x^{\dfrac{11}{2}}}{y^4}\)
