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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{-1}{2}}.q^{\frac{-5}{3}}\\= q^{ \frac{-1}{2} + (\frac{-5}{3}) }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
2. \(q^{\frac{2}{3}}.q^{\frac{-1}{2}}\\= q^{ \frac{2}{3} + (\frac{-1}{2}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
3. \(q^{\frac{2}{3}}.q^{-1}\\= q^{ \frac{2}{3} + (-1) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
4. \(y^{\frac{-2}{5}}.y^{\frac{1}{4}}\\= y^{ \frac{-2}{5} + \frac{1}{4} }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
5. \(x^{\frac{-2}{5}}.x^{\frac{3}{2}}\\= x^{ \frac{-2}{5} + \frac{3}{2} }= x^{\frac{11}{10}}\\=\sqrt[10]{ x^{11} }=|x|.\sqrt[10]{ x }\\---------------\)
6. \(q^{\frac{4}{5}}.q^{\frac{2}{3}}\\= q^{ \frac{4}{5} + \frac{2}{3} }= q^{\frac{22}{15}}\\=\sqrt[15]{ q^{22} }=q.\sqrt[15]{ q^{7} }\\---------------\)
7. \(x^{\frac{2}{3}}.x^{\frac{1}{6}}\\= x^{ \frac{2}{3} + \frac{1}{6} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
8. \(y^{\frac{-2}{3}}.y^{\frac{1}{3}}\\= y^{ \frac{-2}{3} + \frac{1}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
9. \(y^{\frac{-1}{3}}.y^{-1}\\= y^{ \frac{-1}{3} + (-1) }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
10. \(a^{\frac{1}{6}}.a^{\frac{1}{5}}\\= a^{ \frac{1}{6} + \frac{1}{5} }= a^{\frac{11}{30}}\\=\sqrt[30]{ a^{11} }\\---------------\)
11. \(y^{\frac{5}{6}}.y^{\frac{-1}{5}}\\= y^{ \frac{5}{6} + (\frac{-1}{5}) }= y^{\frac{19}{30}}\\=\sqrt[30]{ y^{19} }\\---------------\)
12. \(a^{\frac{-1}{3}}.a^{\frac{-4}{5}}\\= a^{ \frac{-1}{3} + (\frac{-4}{5}) }= a^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ a^{17} }}\\=\frac{1}{a.\sqrt[15]{ a^{2} }}=\frac{1}{a.\sqrt[15]{ a^{2} }} \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a^{2}}\\---------------\)