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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{-4}{3}}.y^{\frac{5}{2}}\\= y^{ \frac{-4}{3} + \frac{5}{2} }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
2. \(a^{\frac{-3}{4}}.a^{\frac{5}{6}}\\= a^{ \frac{-3}{4} + \frac{5}{6} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
3. \(y^{\frac{4}{3}}.y^{-1}\\= y^{ \frac{4}{3} + (-1) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
4. \(q^{\frac{4}{5}}.q^{\frac{-5}{2}}\\= q^{ \frac{4}{5} + (\frac{-5}{2}) }= q^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{7} }}=\frac{1}{|q|.\sqrt[10]{ q^{7} }} \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q^{2}|}\\---------------\)
5. \(y^{\frac{2}{5}}.y^{\frac{2}{5}}\\= y^{ \frac{2}{5} + \frac{2}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
6. \(q^{\frac{-2}{3}}.q^{-1}\\= q^{ \frac{-2}{3} + (-1) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
7. \(a^{\frac{-3}{4}}.a^{\frac{-1}{3}}\\= a^{ \frac{-3}{4} + (\frac{-1}{3}) }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
8. \(a^{\frac{1}{6}}.a^{\frac{1}{3}}\\= a^{ \frac{1}{6} + \frac{1}{3} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
9. \(q^{-1}.q^{\frac{-1}{3}}\\= q^{ -1 + (\frac{-1}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
10. \(y^{\frac{-5}{6}}.y^{1}\\= y^{ \frac{-5}{6} + 1 }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
11. \(a^{\frac{1}{3}}.a^{\frac{5}{4}}\\= a^{ \frac{1}{3} + \frac{5}{4} }= a^{\frac{19}{12}}\\=\sqrt[12]{ a^{19} }=|a|.\sqrt[12]{ a^{7} }\\---------------\)
12. \(q^{-1}.q^{1}\\= q^{ -1 + 1 }= q^{0}\\=1\\---------------\)