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Werk uit m.b.v. de rekenregels

1. \(x^{\frac{1}{3}}.x^{\frac{-3}{2}}\)
2. \(x^{\frac{-1}{2}}.x^{\frac{-4}{3}}\)
3. \(a^{-1}.a^{\frac{1}{6}}\)
4. \(y^{-1}.y^{\frac{5}{3}}\)
5. \(q^{\frac{-1}{2}}.q^{\frac{-3}{5}}\)
6. \(q^{\frac{1}{2}}.q^{1}\)
7. \(y^{\frac{2}{3}}.y^{\frac{3}{4}}\)
8. \(x^{-1}.x^{1}\)
9. \(x^{\frac{5}{6}}.x^{\frac{-1}{3}}\)
10. \(q^{\frac{1}{2}}.q^{\frac{1}{5}}\)
11. \(x^{\frac{5}{6}}.x^{\frac{-5}{4}}\)
12. \(y^{\frac{1}{5}}.y^{\frac{2}{3}}\)

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{1}{3}}.x^{\frac{-3}{2}}\\= x^{ \frac{1}{3} + (\frac{-3}{2}) }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
2. \(x^{\frac{-1}{2}}.x^{\frac{-4}{3}}\\= x^{ \frac{-1}{2} + (\frac{-4}{3}) }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
3. \(a^{-1}.a^{\frac{1}{6}}\\= a^{ -1 + \frac{1}{6} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
4. \(y^{-1}.y^{\frac{5}{3}}\\= y^{ -1 + \frac{5}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
5. \(q^{\frac{-1}{2}}.q^{\frac{-3}{5}}\\= q^{ \frac{-1}{2} + (\frac{-3}{5}) }= q^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[10]{ q }}=\frac{1}{|q|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{2}|}\\---------------\)
6. \(q^{\frac{1}{2}}.q^{1}\\= q^{ \frac{1}{2} + 1 }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
7. \(y^{\frac{2}{3}}.y^{\frac{3}{4}}\\= y^{ \frac{2}{3} + \frac{3}{4} }= y^{\frac{17}{12}}\\=\sqrt[12]{ y^{17} }=|y|.\sqrt[12]{ y^{5} }\\---------------\)
8. \(x^{-1}.x^{1}\\= x^{ -1 + 1 }= x^{0}\\=1\\---------------\)
9. \(x^{\frac{5}{6}}.x^{\frac{-1}{3}}\\= x^{ \frac{5}{6} + (\frac{-1}{3}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(q^{\frac{1}{2}}.q^{\frac{1}{5}}\\= q^{ \frac{1}{2} + \frac{1}{5} }= q^{\frac{7}{10}}\\=\sqrt[10]{ q^{7} }\\---------------\)
11. \(x^{\frac{5}{6}}.x^{\frac{-5}{4}}\\= x^{ \frac{5}{6} + (\frac{-5}{4}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
12. \(y^{\frac{1}{5}}.y^{\frac{2}{3}}\\= y^{ \frac{1}{5} + \frac{2}{3} }= y^{\frac{13}{15}}\\=\sqrt[15]{ y^{13} }\\---------------\)