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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(a^{1}.a^{\frac{1}{3}}\\= a^{ 1 + \frac{1}{3} }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
2. \(a^{1}.a^{\frac{-2}{3}}\\= a^{ 1 + (\frac{-2}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
3. \(y^{\frac{4}{5}}.y^{-1}\\= y^{ \frac{4}{5} + (-1) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
4. \(a^{\frac{2}{3}}.a^{\frac{1}{2}}\\= a^{ \frac{2}{3} + \frac{1}{2} }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
5. \(x^{\frac{-4}{5}}.x^{\frac{1}{6}}\\= x^{ \frac{-4}{5} + \frac{1}{6} }= x^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ x^{19} }}=\frac{1}{\sqrt[30]{ x^{19} }}. \color{purple}{\frac{\sqrt[30]{ x^{11} }}{\sqrt[30]{ x^{11} }}} \\=\frac{\sqrt[30]{ x^{11} }}{|x|}\\---------------\)
6. \(y^{-1}.y^{\frac{5}{3}}\\= y^{ -1 + \frac{5}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
7. \(x^{\frac{-1}{3}}.x^{\frac{3}{2}}\\= x^{ \frac{-1}{3} + \frac{3}{2} }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
8. \(y^{\frac{-1}{6}}.y^{2}\\= y^{ \frac{-1}{6} + 2 }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
9. \(x^{\frac{-3}{4}}.x^{\frac{-3}{4}}\\= x^{ \frac{-3}{4} + (\frac{-3}{4}) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
10. \(q^{\frac{1}{6}}.q^{-2}\\= q^{ \frac{1}{6} + (-2) }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
11. \(a^{\frac{-2}{5}}.a^{\frac{1}{6}}\\= a^{ \frac{-2}{5} + \frac{1}{6} }= a^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ a^{7} }}=\frac{1}{\sqrt[30]{ a^{7} }}. \color{purple}{\frac{\sqrt[30]{ a^{23} }}{\sqrt[30]{ a^{23} }}} \\=\frac{\sqrt[30]{ a^{23} }}{|a|}\\---------------\)
12. \(q^{\frac{-5}{4}}.q^{\frac{5}{6}}\\= q^{ \frac{-5}{4} + \frac{5}{6} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)