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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{1}{2}}.x^{\frac{1}{6}}\\= x^{ \frac{1}{2} + \frac{1}{6} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
2. \(x^{\frac{4}{5}}.x^{2}\\= x^{ \frac{4}{5} + 2 }= x^{\frac{14}{5}}\\=\sqrt[5]{ x^{14} }=x^{2}.\sqrt[5]{ x^{4} }\\---------------\)
3. \(y^{\frac{-2}{5}}.y^{\frac{2}{3}}\\= y^{ \frac{-2}{5} + \frac{2}{3} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
4. \(y^{\frac{1}{3}}.y^{-1}\\= y^{ \frac{1}{3} + (-1) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
5. \(q^{-1}.q^{\frac{3}{5}}\\= q^{ -1 + \frac{3}{5} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
6. \(x^{\frac{2}{3}}.x^{\frac{2}{3}}\\= x^{ \frac{2}{3} + \frac{2}{3} }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
7. \(a^{\frac{5}{6}}.a^{\frac{5}{2}}\\= a^{ \frac{5}{6} + \frac{5}{2} }= a^{\frac{10}{3}}\\=\sqrt[3]{ a^{10} }=a^{3}.\sqrt[3]{ a }\\---------------\)
8. \(y^{\frac{3}{4}}.y^{\frac{-5}{2}}\\= y^{ \frac{3}{4} + (\frac{-5}{2}) }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
9. \(x^{1}.x^{1}\\= x^{ 1 + 1 }= x^{2}\\\\---------------\)
10. \(a^{\frac{-1}{3}}.a^{\frac{-3}{4}}\\= a^{ \frac{-1}{3} + (\frac{-3}{4}) }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
11. \(x^{1}.x^{\frac{-3}{5}}\\= x^{ 1 + (\frac{-3}{5}) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
12. \(q^{\frac{-1}{2}}.q^{\frac{2}{5}}\\= q^{ \frac{-1}{2} + \frac{2}{5} }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)