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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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