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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{1}{6}}.q^{\frac{-3}{2}}\\= q^{ \frac{1}{6} + (\frac{-3}{2}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
2. \(x^{1}.x^{1}\\= x^{ 1 + 1 }= x^{2}\\\\---------------\)
3. \(a^{\frac{2}{3}}.a^{\frac{-2}{3}}\\= a^{ \frac{2}{3} + (\frac{-2}{3}) }= a^{0}\\=1\\---------------\)
4. \(y^{\frac{-4}{3}}.y^{\frac{-1}{2}}\\= y^{ \frac{-4}{3} + (\frac{-1}{2}) }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
5. \(y^{\frac{-4}{5}}.y^{-1}\\= y^{ \frac{-4}{5} + (-1) }= y^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ y^{9} }}\\=\frac{1}{y.\sqrt[5]{ y^{4} }}=\frac{1}{y.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{2}}\\---------------\)
6. \(a^{1}.a^{\frac{-4}{3}}\\= a^{ 1 + (\frac{-4}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
7. \(q^{\frac{5}{4}}.q^{\frac{2}{3}}\\= q^{ \frac{5}{4} + \frac{2}{3} }= q^{\frac{23}{12}}\\=\sqrt[12]{ q^{23} }=|q|.\sqrt[12]{ q^{11} }\\---------------\)
8. \(x^{\frac{-1}{4}}.x^{\frac{2}{3}}\\= x^{ \frac{-1}{4} + \frac{2}{3} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
9. \(a^{\frac{5}{3}}.a^{-1}\\= a^{ \frac{5}{3} + (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
10. \(a^{\frac{-1}{2}}.a^{\frac{3}{5}}\\= a^{ \frac{-1}{2} + \frac{3}{5} }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
11. \(x^{\frac{-5}{3}}.x^{\frac{1}{6}}\\= x^{ \frac{-5}{3} + \frac{1}{6} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
12. \(y^{\frac{4}{3}}.y^{\frac{-1}{4}}\\= y^{ \frac{4}{3} + (\frac{-1}{4}) }= y^{\frac{13}{12}}\\=\sqrt[12]{ y^{13} }=|y|.\sqrt[12]{ y }\\---------------\)