8.
a)
[tex]\sqrt[3]{512} = \sqrt[3]{8^{3}} = 8\\\\\sqrt[3]{-2197} = \sqrt[3]{(-13)^{3}} = -13\\\\\sqrt[3]{-2197000} = \sqrt[3]{(-130)^{3}} = -130[/tex]
b)
[tex]\sqrt[3]{1,331} = \sqrt[3]{1,1^{3}} = 1,1\\\\\sqrt[3]{0,001728} = \sqrt[3]{0,12^{3}} = 0,12\\\\\sqrt[3]{-2197000} = \sqrt[3]{(-130)^{3}} = -130[/tex]
c)
[tex]\sqrt[3]{\frac{343}{2744}} = \frac{\sqrt[3]{343}}{\sqrt[3]{2744}}=\frac{\sqrt[3]{7^{3}}}{\sqrt[3]{14^{3}}}=\frac{7}{14} = \frac{1}{2}\\\\\sqrt[3]{\frac{216}{343}} = \frac{\sqrt[3]{6^{3}}}{\sqrt{7^{3}}} = \frac{6}{7}[/tex]
9.
[tex]a) \ (\sqrt[3]{1728)^{3}} = 1728\\\\b) \ \sqrt[3]{216}\cdot\sqrt[3]{216}\cdot\sqrt[3]{216} = \sqrt[3]{216\cdot216\cdot216} = \sqrt[3]{216^{3}} = 216\\\\c) \ (\sqrt[3]{-5832})^{3} = -5832\\\\d) \ \sqrt[3]{11^{3}} = 11[/tex]
