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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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