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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{2}.y^{\frac{1}{2}}\\= y^{ 2 + \frac{1}{2} }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
2. \(q^{\frac{2}{5}}.q^{\frac{2}{5}}\\= q^{ \frac{2}{5} + \frac{2}{5} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
3. \(q^{\frac{-2}{5}}.q^{\frac{1}{4}}\\= q^{ \frac{-2}{5} + \frac{1}{4} }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
4. \(q^{1}.q^{\frac{-3}{4}}\\= q^{ 1 + (\frac{-3}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
5. \(a^{\frac{1}{2}}.a^{-1}\\= a^{ \frac{1}{2} + (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
6. \(x^{\frac{-1}{4}}.x^{\frac{5}{6}}\\= x^{ \frac{-1}{4} + \frac{5}{6} }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
7. \(q^{2}.q^{1}\\= q^{ 2 + 1 }= q^{3}\\\\---------------\)
8. \(x^{\frac{-1}{2}}.x^{\frac{3}{2}}\\= x^{ \frac{-1}{2} + \frac{3}{2} }= x^{1}\\\\---------------\)
9. \(a^{\frac{2}{3}}.a^{\frac{1}{2}}\\= a^{ \frac{2}{3} + \frac{1}{2} }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
10. \(x^{\frac{5}{4}}.x^{\frac{5}{6}}\\= x^{ \frac{5}{4} + \frac{5}{6} }= x^{\frac{25}{12}}\\=\sqrt[12]{ x^{25} }=|x^{2}|.\sqrt[12]{ x }\\---------------\)
11. \(q^{\frac{-1}{2}}.q^{\frac{-4}{3}}\\= q^{ \frac{-1}{2} + (\frac{-4}{3}) }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
12. \(y^{2}.y^{\frac{-1}{2}}\\= y^{ 2 + (\frac{-1}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)