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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-1}{3}}.x^{\frac{4}{3}}\\= x^{ \frac{-1}{3} + \frac{4}{3} }= x^{1}\\\\---------------\)
2. \(x^{\frac{-2}{3}}.x^{-1}\\= x^{ \frac{-2}{3} + (-1) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
3. \(q^{\frac{-1}{3}}.q^{\frac{-3}{2}}\\= q^{ \frac{-1}{3} + (\frac{-3}{2}) }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
4. \(x^{\frac{2}{3}}.x^{-1}\\= x^{ \frac{2}{3} + (-1) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
5. \(a^{\frac{-1}{6}}.a^{\frac{-1}{3}}\\= a^{ \frac{-1}{6} + (\frac{-1}{3}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
6. \(y^{\frac{-5}{4}}.y^{\frac{2}{3}}\\= y^{ \frac{-5}{4} + \frac{2}{3} }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
7. \(a^{\frac{-1}{3}}.a^{\frac{1}{2}}\\= a^{ \frac{-1}{3} + \frac{1}{2} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
8. \(y^{\frac{-1}{3}}.y^{\frac{-1}{4}}\\= y^{ \frac{-1}{3} + (\frac{-1}{4}) }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
9. \(x^{-2}.x^{-2}\\= x^{ -2 + (-2) }= x^{-4}\\=\frac{1}{x^{4}}\\---------------\)
10. \(q^{\frac{-2}{3}}.q^{\frac{1}{4}}\\= q^{ \frac{-2}{3} + \frac{1}{4} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
11. \(x^{\frac{-2}{3}}.x^{\frac{-3}{5}}\\= x^{ \frac{-2}{3} + (\frac{-3}{5}) }= x^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ x^{19} }}\\=\frac{1}{x.\sqrt[15]{ x^{4} }}=\frac{1}{x.\sqrt[15]{ x^{4} }} \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x^{2}}\\---------------\)
12. \(x^{\frac{-4}{3}}.x^{\frac{2}{3}}\\= x^{ \frac{-4}{3} + \frac{2}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)