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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{3}{4}}.x^{\frac{-1}{4}}\\= x^{ \frac{3}{4} + (\frac{-1}{4}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
2. \(q^{\frac{-5}{6}}.q^{\frac{-2}{3}}\\= q^{ \frac{-5}{6} + (\frac{-2}{3}) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
3. \(x^{\frac{4}{3}}.x^{-1}\\= x^{ \frac{4}{3} + (-1) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
4. \(x^{\frac{-1}{4}}.x^{\frac{1}{5}}\\= x^{ \frac{-1}{4} + \frac{1}{5} }= x^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ x }}=\frac{1}{\sqrt[20]{ x }}. \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x|}\\---------------\)
5. \(y^{-1}.y^{\frac{-1}{2}}\\= y^{ -1 + (\frac{-1}{2}) }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
6. \(x^{-1}.x^{\frac{-3}{2}}\\= x^{ -1 + (\frac{-3}{2}) }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
7. \(a^{\frac{-2}{3}}.a^{\frac{-5}{4}}\\= a^{ \frac{-2}{3} + (\frac{-5}{4}) }= a^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ a^{23} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{11} }}=\frac{1}{|a|.\sqrt[12]{ a^{11} }} \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a^{2}|}\\---------------\)
8. \(q^{\frac{5}{6}}.q^{\frac{-3}{5}}\\= q^{ \frac{5}{6} + (\frac{-3}{5}) }= q^{\frac{7}{30}}\\=\sqrt[30]{ q^{7} }\\---------------\)
9. \(x^{\frac{-2}{3}}.x^{\frac{1}{4}}\\= x^{ \frac{-2}{3} + \frac{1}{4} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
10. \(x^{\frac{1}{2}}.x^{\frac{4}{3}}\\= x^{ \frac{1}{2} + \frac{4}{3} }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
11. \(x^{\frac{1}{2}}.x^{\frac{-3}{5}}\\= x^{ \frac{1}{2} + (\frac{-3}{5}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
12. \(y^{-2}.y^{\frac{1}{3}}\\= y^{ -2 + \frac{1}{3} }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)