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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{-1}.q^{\frac{4}{3}}\\= q^{ -1 + \frac{4}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
2. \(y^{\frac{-1}{2}}.y^{\frac{-1}{2}}\\= y^{ \frac{-1}{2} + (\frac{-1}{2}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
3. \(a^{\frac{5}{6}}.a^{\frac{3}{5}}\\= a^{ \frac{5}{6} + \frac{3}{5} }= a^{\frac{43}{30}}\\=\sqrt[30]{ a^{43} }=|a|.\sqrt[30]{ a^{13} }\\---------------\)
4. \(q^{\frac{-3}{5}}.q^{\frac{2}{5}}\\= q^{ \frac{-3}{5} + \frac{2}{5} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
5. \(q^{-2}.q^{\frac{5}{6}}\\= q^{ -2 + \frac{5}{6} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
6. \(y^{\frac{-5}{4}}.y^{\frac{-1}{3}}\\= y^{ \frac{-5}{4} + (\frac{-1}{3}) }= y^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{7} }}=\frac{1}{|y|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{2}|}\\---------------\)
7. \(y^{-1}.y^{1}\\= y^{ -1 + 1 }= y^{0}\\=1\\---------------\)
8. \(x^{\frac{1}{2}}.x^{\frac{-4}{5}}\\= x^{ \frac{1}{2} + (\frac{-4}{5}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
9. \(a^{\frac{1}{2}}.a^{\frac{5}{3}}\\= a^{ \frac{1}{2} + \frac{5}{3} }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
10. \(a^{\frac{3}{4}}.a^{\frac{3}{5}}\\= a^{ \frac{3}{4} + \frac{3}{5} }= a^{\frac{27}{20}}\\=\sqrt[20]{ a^{27} }=|a|.\sqrt[20]{ a^{7} }\\---------------\)
11. \(a^{\frac{5}{6}}.a^{\frac{-1}{3}}\\= a^{ \frac{5}{6} + (\frac{-1}{3}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(x^{-1}.x^{\frac{-1}{2}}\\= x^{ -1 + (\frac{-1}{2}) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)