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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{2}{5}}.x^{\frac{2}{3}}\\= x^{ \frac{2}{5} + \frac{2}{3} }= x^{\frac{16}{15}}\\=\sqrt[15]{ x^{16} }=x.\sqrt[15]{ x }\\---------------\)
2. \(y^{\frac{-5}{2}}.y^{-1}\\= y^{ \frac{-5}{2} + (-1) }= y^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ y^{7} } }\\=\frac{1}{|y^{3}|. \sqrt{ y } }=\frac{1}{|y^{3}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{4}|}\\---------------\)
3. \(y^{\frac{3}{4}}.y^{\frac{1}{6}}\\= y^{ \frac{3}{4} + \frac{1}{6} }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
4. \(q^{\frac{4}{3}}.q^{\frac{-3}{4}}\\= q^{ \frac{4}{3} + (\frac{-3}{4}) }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
5. \(q^{\frac{-5}{2}}.q^{\frac{2}{5}}\\= q^{ \frac{-5}{2} + \frac{2}{5} }= q^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ q^{21} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q }}=\frac{1}{|q^{2}|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{3}|}\\---------------\)
6. \(y^{\frac{3}{5}}.y^{-1}\\= y^{ \frac{3}{5} + (-1) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
7. \(y^{\frac{-1}{5}}.y^{\frac{-1}{4}}\\= y^{ \frac{-1}{5} + (\frac{-1}{4}) }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
8. \(q^{\frac{5}{4}}.q^{\frac{2}{5}}\\= q^{ \frac{5}{4} + \frac{2}{5} }= q^{\frac{33}{20}}\\=\sqrt[20]{ q^{33} }=|q|.\sqrt[20]{ q^{13} }\\---------------\)
9. \(x^{2}.x^{\frac{4}{5}}\\= x^{ 2 + \frac{4}{5} }= x^{\frac{14}{5}}\\=\sqrt[5]{ x^{14} }=x^{2}.\sqrt[5]{ x^{4} }\\---------------\)
10. \(y^{\frac{-3}{5}}.y^{\frac{2}{5}}\\= y^{ \frac{-3}{5} + \frac{2}{5} }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
11. \(q^{\frac{2}{3}}.q^{\frac{-3}{4}}\\= q^{ \frac{2}{3} + (\frac{-3}{4}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
12. \(y^{-1}.y^{\frac{-1}{4}}\\= y^{ -1 + (\frac{-1}{4}) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)