a) [tex]\frac{1}{\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} } = \frac{\sqrt{2} }{\sqrt{2*2} } = \frac{\sqrt{2} }{2}[/tex]
b) [tex]\frac{2}{\sqrt[3]{2} } * \frac{\sqrt[3]{4} }{\sqrt[3]{4} } = \frac{2\sqrt[3]{4} }{\sqrt[3]{8} } = \frac{2\sqrt[3]{4} }{2} =\sqrt[3]{4}[/tex]
c) [tex]\frac{3}{\sqrt[3]{3} } * \frac{\sqrt[3]{9} }{\sqrt[3]{9} } = \frac{3\sqrt[3]{9} }{\sqrt[3]{27} } = \frac{3\sqrt[3]{9} }{3} = \sqrt[3]{9}[/tex]
d) [tex]\frac{\sqrt{10} }{5\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} } = \frac{\sqrt{20} }{5\sqrt{4} } = \frac{2\sqrt{5} }{10} = \frac{\sqrt{5} }{5}[/tex]
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a) [tex]\frac{1}{\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} } = \frac{\sqrt{2} }{\sqrt{2*2} } = \frac{\sqrt{2} }{2}[/tex]
b) [tex]\frac{2}{\sqrt[3]{2} } * \frac{\sqrt[3]{4} }{\sqrt[3]{4} } = \frac{2\sqrt[3]{4} }{\sqrt[3]{8} } = \frac{2\sqrt[3]{4} }{2} =\sqrt[3]{4}[/tex]
c) [tex]\frac{3}{\sqrt[3]{3} } * \frac{\sqrt[3]{9} }{\sqrt[3]{9} } = \frac{3\sqrt[3]{9} }{\sqrt[3]{27} } = \frac{3\sqrt[3]{9} }{3} = \sqrt[3]{9}[/tex]
d) [tex]\frac{\sqrt{10} }{5\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} } = \frac{\sqrt{20} }{5\sqrt{4} } = \frac{2\sqrt{5} }{10} = \frac{\sqrt{5} }{5}[/tex]