8.
[tex]a) \ \sqrt[3]{32}\cdot\sqrt[3]{2} = \sqrt[3]{32\cdot2} = \sqrt[3]{64} = \sqrt[3]{4^{3}} =\boxed{4}\\\\b) \ \frac{\sqrt[3]{27}}{\sqrt[3]{-8}} =\frac{\sqrt[3]{3^{3}}}{\sqrt[3]{(-2)^{3}}} = -\frac{3}{2} =\boxed{-1\frac{1}{2}}[/tex]
9.
[tex]\sqrt[3]{\frac{1}{27}}\cdot\sqrt[3]{8}-\frac{\sqrt{169}}{\sqrt{100}} = \sqrt[3]{\frac{1}{27}\cdot8}}-\frac{13}{10} = \sqrt[3]{\frac{8}{27}} -\frac{13}{10} = \frac{2}{3}-\frac{13}{10} =\frac{20}{30}-\frac{39}{30}=\boxed{-\frac{19}{30}}[/tex]
10.
[tex]a) \ 6t - (4x+2y-5) = 6t-4x-2y+5\\\\b) \ 4k+2(x-3y+t) = 4k+2x-6y+2t\\\\c) \ 5-(8m-3k)\cdot4=5-(8m\cdot4-3k\cdot4) = 5-32m+12k\\\\d) \ 8x-(15k+20m):5 = 8x-(15k:5+20m:5) = 8x-3k-4m[/tex]
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Verified answer
8.
[tex]a) \ \sqrt[3]{32}\cdot\sqrt[3]{2} = \sqrt[3]{32\cdot2} = \sqrt[3]{64} = \sqrt[3]{4^{3}} =\boxed{4}\\\\b) \ \frac{\sqrt[3]{27}}{\sqrt[3]{-8}} =\frac{\sqrt[3]{3^{3}}}{\sqrt[3]{(-2)^{3}}} = -\frac{3}{2} =\boxed{-1\frac{1}{2}}[/tex]
9.
[tex]\sqrt[3]{\frac{1}{27}}\cdot\sqrt[3]{8}-\frac{\sqrt{169}}{\sqrt{100}} = \sqrt[3]{\frac{1}{27}\cdot8}}-\frac{13}{10} = \sqrt[3]{\frac{8}{27}} -\frac{13}{10} = \frac{2}{3}-\frac{13}{10} =\frac{20}{30}-\frac{39}{30}=\boxed{-\frac{19}{30}}[/tex]
10.
[tex]a) \ 6t - (4x+2y-5) = 6t-4x-2y+5\\\\b) \ 4k+2(x-3y+t) = 4k+2x-6y+2t\\\\c) \ 5-(8m-3k)\cdot4=5-(8m\cdot4-3k\cdot4) = 5-32m+12k\\\\d) \ 8x-(15k+20m):5 = 8x-(15k:5+20m:5) = 8x-3k-4m[/tex]