[tex]a=\sqrt[3]{3}\ \ ,\ \ b=\sqrt[2]{32}\ \ ,\ \ c=\sqrt[2]{2}\\\\\\\lbrack(a)^b\rbrack^c=[(\sqrt[3]{3})^{\sqrt{32}}]^{\sqrt{2}}=(\sqrt[3]{3})^{\sqrt{32}\cdot\sqrt{2}}=(\sqrt[3]{3})^{\sqrt{64} }=(\sqrt[3]{3})^8=\sqrt[3]{3^8}=\sqrt[3]{3^6\cdot3^2}=\\\\=\sqrt[3]{3^6}\cdot\sqrt[3]{3^2}=3^{\frac{6}{3}}\cdot\sqrt[3]{3^2}=3^2\cdot\sqrt[3]{3^2}=9\sqrt[3]{9}[/tex]
[tex]\sqrt[2]{32}=\sqrt{32}\ \ ,\ \ \sqrt[2]{2}=\sqrt{2}[/tex]
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[tex]a=\sqrt[3]{3}\ \ ,\ \ b=\sqrt[2]{32}\ \ ,\ \ c=\sqrt[2]{2}\\\\\\\lbrack(a)^b\rbrack^c=[(\sqrt[3]{3})^{\sqrt{32}}]^{\sqrt{2}}=(\sqrt[3]{3})^{\sqrt{32}\cdot\sqrt{2}}=(\sqrt[3]{3})^{\sqrt{64} }=(\sqrt[3]{3})^8=\sqrt[3]{3^8}=\sqrt[3]{3^6\cdot3^2}=\\\\=\sqrt[3]{3^6}\cdot\sqrt[3]{3^2}=3^{\frac{6}{3}}\cdot\sqrt[3]{3^2}=3^2\cdot\sqrt[3]{3^2}=9\sqrt[3]{9}[/tex]
[tex]\sqrt[2]{32}=\sqrt{32}\ \ ,\ \ \sqrt[2]{2}=\sqrt{2}[/tex]