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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{4}{5}}.q^{\frac{-1}{5}}\\= q^{ \frac{4}{5} + (\frac{-1}{5}) }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
2. \(a^{\frac{-5}{3}}.a^{\frac{2}{5}}\\= a^{ \frac{-5}{3} + \frac{2}{5} }= a^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ a^{19} }}\\=\frac{1}{a.\sqrt[15]{ a^{4} }}=\frac{1}{a.\sqrt[15]{ a^{4} }} \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a^{2}}\\---------------\)
3. \(x^{-1}.x^{\frac{-2}{3}}\\= x^{ -1 + (\frac{-2}{3}) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
4. \(y^{\frac{-3}{5}}.y^{\frac{-1}{3}}\\= y^{ \frac{-3}{5} + (\frac{-1}{3}) }= y^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ y^{14} }}=\frac{1}{\sqrt[15]{ y^{14} }}. \color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y}\\---------------\)
5. \(q^{1}.q^{\frac{5}{6}}\\= q^{ 1 + \frac{5}{6} }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
6. \(q^{\frac{-5}{2}}.q^{\frac{1}{6}}\\= q^{ \frac{-5}{2} + \frac{1}{6} }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
7. \(a^{\frac{-5}{2}}.a^{\frac{1}{2}}\\= a^{ \frac{-5}{2} + \frac{1}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
8. \(a^{\frac{-4}{3}}.a^{\frac{-4}{3}}\\= a^{ \frac{-4}{3} + (\frac{-4}{3}) }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
9. \(a^{\frac{4}{3}}.a^{\frac{-5}{4}}\\= a^{ \frac{4}{3} + (\frac{-5}{4}) }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
10. \(q^{\frac{-4}{3}}.q^{\frac{-2}{3}}\\= q^{ \frac{-4}{3} + (\frac{-2}{3}) }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
11. \(q^{\frac{1}{2}}.q^{-1}\\= q^{ \frac{1}{2} + (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
12. \(a^{1}.a^{\frac{-1}{2}}\\= a^{ 1 + (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)