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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{-2}{5}}.q^{\frac{-5}{2}}\\= q^{ \frac{-2}{5} + (\frac{-5}{2}) }= q^{\frac{-29}{10}}\\=\frac{1}{\sqrt[10]{ q^{29} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q^{9} }}=\frac{1}{|q^{2}|.\sqrt[10]{ q^{9} }} \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q^{3}|}\\---------------\)
2. \(y^{\frac{2}{3}}.y^{\frac{3}{4}}\\= y^{ \frac{2}{3} + \frac{3}{4} }= y^{\frac{17}{12}}\\=\sqrt[12]{ y^{17} }=|y|.\sqrt[12]{ y^{5} }\\---------------\)
3. \(x^{1}.x^{\frac{3}{5}}\\= x^{ 1 + \frac{3}{5} }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
4. \(a^{\frac{2}{5}}.a^{\frac{-4}{3}}\\= a^{ \frac{2}{5} + (\frac{-4}{3}) }= a^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ a^{14} }}=\frac{1}{\sqrt[15]{ a^{14} }}. \color{purple}{\frac{\sqrt[15]{ a }}{\sqrt[15]{ a }}} \\=\frac{\sqrt[15]{ a }}{a}\\---------------\)
5. \(y^{\frac{-5}{6}}.y^{\frac{5}{2}}\\= y^{ \frac{-5}{6} + \frac{5}{2} }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
6. \(y^{-2}.y^{\frac{-2}{5}}\\= y^{ -2 + (\frac{-2}{5}) }= y^{\frac{-12}{5}}\\=\frac{1}{\sqrt[5]{ y^{12} }}\\=\frac{1}{y^{2}.\sqrt[5]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{3}}\\---------------\)
7. \(x^{1}.x^{\frac{1}{6}}\\= x^{ 1 + \frac{1}{6} }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
8. \(q^{\frac{-1}{3}}.q^{\frac{-1}{2}}\\= q^{ \frac{-1}{3} + (\frac{-1}{2}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
9. \(x^{\frac{4}{3}}.x^{\frac{2}{3}}\\= x^{ \frac{4}{3} + \frac{2}{3} }= x^{2}\\\\---------------\)
10. \(x^{\frac{-5}{4}}.x^{\frac{-1}{4}}\\= x^{ \frac{-5}{4} + (\frac{-1}{4}) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
11. \(a^{\frac{3}{2}}.a^{\frac{-5}{6}}\\= a^{ \frac{3}{2} + (\frac{-5}{6}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
12. \(x^{1}.x^{\frac{-5}{3}}\\= x^{ 1 + (\frac{-5}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)