[tex]\sqrt[4]{4^3}*\sqrt[4]9*\sqrt[4]{6^6}=\sqrt[4]{4^3*9*6^6}=\sqrt[4]{(2^2)^3*3^2*(2*3)^6}=\\\\=\sqrt[4]{2^6*3^2*2^6*3^6}=\sqrt[4]{2^6*2^6*3^2*3^6}=\sqrt[4]{2^{6+6}*3^{2+6}}=\sqrt[4]{2^{12}*3^{8}}=\\\\=\sqrt[4]{2^{12}}*\sqrt[4]{3^{8}}=\sqrt[4]{(2^3)^4}*\sqrt[4]{(3^2)^4}=\sqrt[4]{8^4}*\sqrt[4]{9^4}=8*9=72[/tex]
[tex]3^{\frac{1}{2}}*9^\frac{1}{3}}*\sqrt3=3^{\frac{1}{2}}*(3^2)^\frac{1}{3}}*3^{\frac{1}{2}}=3^{\frac{1}{2}}*3^\frac{2}{3}*3^{\frac{1}{2}}=3^{\frac{1}{2}+\frac{2}{3}+\frac{1}{2}}=3^{1+\frac{2}{3}}=3^{1\frac{2}{3}}[/tex]
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[tex]\sqrt[4]{4^3}*\sqrt[4]9*\sqrt[4]{6^6}=\sqrt[4]{4^3*9*6^6}=\sqrt[4]{(2^2)^3*3^2*(2*3)^6}=\\\\=\sqrt[4]{2^6*3^2*2^6*3^6}=\sqrt[4]{2^6*2^6*3^2*3^6}=\sqrt[4]{2^{6+6}*3^{2+6}}=\sqrt[4]{2^{12}*3^{8}}=\\\\=\sqrt[4]{2^{12}}*\sqrt[4]{3^{8}}=\sqrt[4]{(2^3)^4}*\sqrt[4]{(3^2)^4}=\sqrt[4]{8^4}*\sqrt[4]{9^4}=8*9=72[/tex]
[tex]3^{\frac{1}{2}}*9^\frac{1}{3}}*\sqrt3=3^{\frac{1}{2}}*(3^2)^\frac{1}{3}}*3^{\frac{1}{2}}=3^{\frac{1}{2}}*3^\frac{2}{3}*3^{\frac{1}{2}}=3^{\frac{1}{2}+\frac{2}{3}+\frac{1}{2}}=3^{1+\frac{2}{3}}=3^{1\frac{2}{3}}[/tex]
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