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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{-1}.q^{\frac{-1}{2}}\\= q^{ -1 + (\frac{-1}{2}) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
2. \(y^{\frac{5}{2}}.y^{\frac{5}{4}}\\= y^{ \frac{5}{2} + \frac{5}{4} }= y^{\frac{15}{4}}\\=\sqrt[4]{ y^{15} }=|y^{3}|.\sqrt[4]{ y^{3} }\\---------------\)
3. \(q^{\frac{1}{3}}.q^{\frac{3}{2}}\\= q^{ \frac{1}{3} + \frac{3}{2} }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
4. \(a^{\frac{2}{5}}.a^{-1}\\= a^{ \frac{2}{5} + (-1) }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
5. \(y^{\frac{-1}{2}}.y^{\frac{-2}{3}}\\= y^{ \frac{-1}{2} + (\frac{-2}{3}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
6. \(q^{\frac{-1}{6}}.q^{\frac{-1}{2}}\\= q^{ \frac{-1}{6} + (\frac{-1}{2}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
7. \(x^{\frac{-1}{2}}.x^{\frac{2}{3}}\\= x^{ \frac{-1}{2} + \frac{2}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
8. \(x^{-1}.x^{\frac{-5}{6}}\\= x^{ -1 + (\frac{-5}{6}) }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
9. \(x^{\frac{1}{5}}.x^{\frac{4}{3}}\\= x^{ \frac{1}{5} + \frac{4}{3} }= x^{\frac{23}{15}}\\=\sqrt[15]{ x^{23} }=x.\sqrt[15]{ x^{8} }\\---------------\)
10. \(q^{2}.q^{\frac{5}{2}}\\= q^{ 2 + \frac{5}{2} }= q^{\frac{9}{2}}\\= \sqrt{ q^{9} } =|q^{4}|. \sqrt{ q } \\---------------\)
11. \(q^{\frac{1}{4}}.q^{1}\\= q^{ \frac{1}{4} + 1 }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
12. \(a^{\frac{3}{5}}.a^{\frac{-2}{3}}\\= a^{ \frac{3}{5} + (\frac{-2}{3}) }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)