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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(a^{\frac{-2}{3}}.a^{-1}\\= a^{ \frac{-2}{3} + (-1) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
2. \(q^{\frac{1}{2}}.q^{\frac{-2}{3}}\\= q^{ \frac{1}{2} + (\frac{-2}{3}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
3. \(y^{1}.y^{2}\\= y^{ 1 + 2 }= y^{3}\\\\---------------\)
4. \(q^{\frac{3}{5}}.q^{\frac{-1}{3}}\\= q^{ \frac{3}{5} + (\frac{-1}{3}) }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
5. \(y^{-1}.y^{-1}\\= y^{ -1 + (-1) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
6. \(a^{\frac{-1}{2}}.a^{\frac{-5}{3}}\\= a^{ \frac{-1}{2} + (\frac{-5}{3}) }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
7. \(a^{\frac{-1}{6}}.a^{2}\\= a^{ \frac{-1}{6} + 2 }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
8. \(y^{\frac{-5}{2}}.y^{\frac{-2}{5}}\\= y^{ \frac{-5}{2} + (\frac{-2}{5}) }= y^{\frac{-29}{10}}\\=\frac{1}{\sqrt[10]{ y^{29} }}\\=\frac{1}{|y^{2}|.\sqrt[10]{ y^{9} }}=\frac{1}{|y^{2}|.\sqrt[10]{ y^{9} }} \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y^{3}|}\\---------------\)
9. \(a^{\frac{1}{3}}.a^{\frac{2}{5}}\\= a^{ \frac{1}{3} + \frac{2}{5} }= a^{\frac{11}{15}}\\=\sqrt[15]{ a^{11} }\\---------------\)
10. \(q^{\frac{1}{2}}.q^{2}\\= q^{ \frac{1}{2} + 2 }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
11. \(x^{\frac{2}{3}}.x^{\frac{3}{5}}\\= x^{ \frac{2}{3} + \frac{3}{5} }= x^{\frac{19}{15}}\\=\sqrt[15]{ x^{19} }=x.\sqrt[15]{ x^{4} }\\---------------\)
12. \(q^{\frac{2}{3}}.q^{\frac{-1}{3}}\\= q^{ \frac{2}{3} + (\frac{-1}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)