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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{5}{3}}.q^{2}\\= q^{ \frac{5}{3} + 2 }= q^{\frac{11}{3}}\\=\sqrt[3]{ q^{11} }=q^{3}.\sqrt[3]{ q^{2} }\\---------------\)
2. \(q^{\frac{-1}{4}}.q^{\frac{5}{3}}\\= q^{ \frac{-1}{4} + \frac{5}{3} }= q^{\frac{17}{12}}\\=\sqrt[12]{ q^{17} }=|q|.\sqrt[12]{ q^{5} }\\---------------\)
3. \(y^{\frac{1}{3}}.y^{-1}\\= y^{ \frac{1}{3} + (-1) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
4. \(a^{\frac{4}{5}}.a^{\frac{-4}{3}}\\= a^{ \frac{4}{5} + (\frac{-4}{3}) }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
5. \(a^{\frac{1}{2}}.a^{\frac{-4}{3}}\\= a^{ \frac{1}{2} + (\frac{-4}{3}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
6. \(x^{\frac{1}{4}}.x^{\frac{1}{3}}\\= x^{ \frac{1}{4} + \frac{1}{3} }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
7. \(a^{\frac{5}{3}}.a^{1}\\= a^{ \frac{5}{3} + 1 }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
8. \(q^{\frac{5}{2}}.q^{\frac{2}{3}}\\= q^{ \frac{5}{2} + \frac{2}{3} }= q^{\frac{19}{6}}\\=\sqrt[6]{ q^{19} }=|q^{3}|.\sqrt[6]{ q }\\---------------\)
9. \(a^{-1}.a^{-1}\\= a^{ -1 + (-1) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
10. \(q^{\frac{-4}{3}}.q^{\frac{5}{4}}\\= q^{ \frac{-4}{3} + \frac{5}{4} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
11. \(y^{\frac{1}{2}}.y^{-2}\\= y^{ \frac{1}{2} + (-2) }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
12. \(x^{\frac{-1}{2}}.x^{1}\\= x^{ \frac{-1}{2} + 1 }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)