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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-2}{5}}.x^{\frac{5}{6}}\\= x^{ \frac{-2}{5} + \frac{5}{6} }= x^{\frac{13}{30}}\\=\sqrt[30]{ x^{13} }\\---------------\)
2. \(y^{\frac{-3}{2}}.y^{\frac{1}{3}}\\= y^{ \frac{-3}{2} + \frac{1}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
3. \(x^{\frac{5}{4}}.x^{\frac{-1}{2}}\\= x^{ \frac{5}{4} + (\frac{-1}{2}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
4. \(x^{\frac{-1}{4}}.x^{\frac{-4}{5}}\\= x^{ \frac{-1}{4} + (\frac{-4}{5}) }= x^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ x^{21} }}\\=\frac{1}{|x|.\sqrt[20]{ x }}=\frac{1}{|x|.\sqrt[20]{ x }} \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x^{2}|}\\---------------\)
5. \(x^{\frac{-5}{2}}.x^{\frac{4}{5}}\\= x^{ \frac{-5}{2} + \frac{4}{5} }= x^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[10]{ x^{7} }}=\frac{1}{|x|.\sqrt[10]{ x^{7} }} \color{purple}{\frac{\sqrt[10]{ x^{3} }}{\sqrt[10]{ x^{3} }}} \\=\frac{\sqrt[10]{ x^{3} }}{|x^{2}|}\\---------------\)
6. \(a^{-1}.a^{\frac{-1}{2}}\\= a^{ -1 + (\frac{-1}{2}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
7. \(y^{\frac{-1}{2}}.y^{\frac{1}{2}}\\= y^{ \frac{-1}{2} + \frac{1}{2} }= y^{0}\\=1\\---------------\)
8. \(q^{\frac{-1}{4}}.q^{1}\\= q^{ \frac{-1}{4} + 1 }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
9. \(y^{\frac{-5}{2}}.y^{\frac{3}{2}}\\= y^{ \frac{-5}{2} + \frac{3}{2} }= y^{-1}\\=\frac{1}{y}\\---------------\)
10. \(x^{1}.x^{\frac{3}{5}}\\= x^{ 1 + \frac{3}{5} }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
11. \(x^{\frac{-1}{5}}.x^{\frac{-5}{6}}\\= x^{ \frac{-1}{5} + (\frac{-5}{6}) }= x^{\frac{-31}{30}}\\=\frac{1}{\sqrt[30]{ x^{31} }}\\=\frac{1}{|x|.\sqrt[30]{ x }}=\frac{1}{|x|.\sqrt[30]{ x }} \color{purple}{\frac{\sqrt[30]{ x^{29} }}{\sqrt[30]{ x^{29} }}} \\=\frac{\sqrt[30]{ x^{29} }}{|x^{2}|}\\---------------\)
12. \(a^{\frac{-1}{6}}.a^{\frac{-1}{4}}\\= a^{ \frac{-1}{6} + (\frac{-1}{4}) }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)