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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{-1}{5}}.y^{\frac{-2}{5}}\\= y^{ \frac{-1}{5} + (\frac{-2}{5}) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
2. \(y^{\frac{-1}{2}}.y^{\frac{-1}{6}}\\= y^{ \frac{-1}{2} + (\frac{-1}{6}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
3. \(q^{\frac{-5}{2}}.q^{\frac{1}{2}}\\= q^{ \frac{-5}{2} + \frac{1}{2} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
4. \(y^{-1}.y^{\frac{4}{3}}\\= y^{ -1 + \frac{4}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
5. \(q^{\frac{4}{3}}.q^{\frac{-3}{2}}\\= q^{ \frac{4}{3} + (\frac{-3}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
6. \(y^{\frac{-2}{3}}.y^{-1}\\= y^{ \frac{-2}{3} + (-1) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
7. \(y^{\frac{-1}{3}}.y^{2}\\= y^{ \frac{-1}{3} + 2 }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
8. \(q^{\frac{5}{2}}.q^{\frac{-1}{2}}\\= q^{ \frac{5}{2} + (\frac{-1}{2}) }= q^{2}\\\\---------------\)
9. \(x^{\frac{-5}{4}}.x^{\frac{-5}{3}}\\= x^{ \frac{-5}{4} + (\frac{-5}{3}) }= x^{\frac{-35}{12}}\\=\frac{1}{\sqrt[12]{ x^{35} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x^{11} }}=\frac{1}{|x^{2}|.\sqrt[12]{ x^{11} }} \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x^{3}|}\\---------------\)
10. \(x^{\frac{-1}{3}}.x^{\frac{3}{2}}\\= x^{ \frac{-1}{3} + \frac{3}{2} }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
11. \(x^{\frac{-3}{4}}.x^{\frac{5}{3}}\\= x^{ \frac{-3}{4} + \frac{5}{3} }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)
12. \(q^{\frac{1}{5}}.q^{\frac{1}{4}}\\= q^{ \frac{1}{5} + \frac{1}{4} }= q^{\frac{9}{20}}\\=\sqrt[20]{ q^{9} }\\---------------\)