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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-3}{2}}.x^{\frac{1}{2}}\\= x^{ \frac{-3}{2} + \frac{1}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
2. \(y^{\frac{4}{3}}.y^{\frac{1}{2}}\\= y^{ \frac{4}{3} + \frac{1}{2} }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
3. \(x^{-2}.x^{\frac{-5}{2}}\\= x^{ -2 + (\frac{-5}{2}) }= x^{\frac{-9}{2}}\\=\frac{1}{ \sqrt{ x^{9} } }\\=\frac{1}{|x^{4}|. \sqrt{ x } }=\frac{1}{|x^{4}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{5}|}\\---------------\)
4. \(q^{-1}.q^{-2}\\= q^{ -1 + (-2) }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
5. \(a^{\frac{-5}{2}}.a^{\frac{-1}{3}}\\= a^{ \frac{-5}{2} + (\frac{-1}{3}) }= a^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ a^{17} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a^{5} }}=\frac{1}{|a^{2}|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{3}|}\\---------------\)
6. \(q^{\frac{-1}{2}}.q^{\frac{1}{3}}\\= q^{ \frac{-1}{2} + \frac{1}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
7. \(q^{\frac{-2}{3}}.q^{\frac{3}{5}}\\= q^{ \frac{-2}{3} + \frac{3}{5} }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
8. \(x^{\frac{-5}{6}}.x^{\frac{-3}{2}}\\= x^{ \frac{-5}{6} + (\frac{-3}{2}) }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
9. \(a^{\frac{-1}{3}}.a^{\frac{-3}{5}}\\= a^{ \frac{-1}{3} + (\frac{-3}{5}) }= a^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ a^{14} }}=\frac{1}{\sqrt[15]{ a^{14} }}. \color{purple}{\frac{\sqrt[15]{ a }}{\sqrt[15]{ a }}} \\=\frac{\sqrt[15]{ a }}{a}\\---------------\)
10. \(a^{\frac{3}{5}}.a^{\frac{-1}{6}}\\= a^{ \frac{3}{5} + (\frac{-1}{6}) }= a^{\frac{13}{30}}\\=\sqrt[30]{ a^{13} }\\---------------\)
11. \(q^{\frac{1}{3}}.q^{\frac{-3}{4}}\\= q^{ \frac{1}{3} + (\frac{-3}{4}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
12. \(y^{\frac{1}{6}}.y^{\frac{3}{4}}\\= y^{ \frac{1}{6} + \frac{3}{4} }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)