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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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