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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{4}{5}}.x^{-1}\\= x^{ \frac{4}{5} + (-1) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
2. \(a^{\frac{2}{3}}.a^{\frac{1}{3}}\\= a^{ \frac{2}{3} + \frac{1}{3} }= a^{1}\\\\---------------\)
3. \(q^{-1}.q^{\frac{1}{2}}\\= q^{ -1 + \frac{1}{2} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
4. \(x^{\frac{-4}{5}}.x^{\frac{-5}{2}}\\= x^{ \frac{-4}{5} + (\frac{-5}{2}) }= x^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ x^{33} }}\\=\frac{1}{|x^{3}|.\sqrt[10]{ x^{3} }}=\frac{1}{|x^{3}|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{4}|}\\---------------\)
5. \(q^{\frac{-2}{3}}.q^{\frac{-2}{3}}\\= q^{ \frac{-2}{3} + (\frac{-2}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
6. \(y^{\frac{4}{3}}.y^{\frac{-2}{3}}\\= y^{ \frac{4}{3} + (\frac{-2}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
7. \(x^{\frac{-1}{6}}.x^{\frac{-1}{2}}\\= x^{ \frac{-1}{6} + (\frac{-1}{2}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
8. \(a^{\frac{5}{4}}.a^{2}\\= a^{ \frac{5}{4} + 2 }= a^{\frac{13}{4}}\\=\sqrt[4]{ a^{13} }=|a^{3}|.\sqrt[4]{ a }\\---------------\)
9. \(q^{\frac{1}{6}}.q^{\frac{-1}{3}}\\= q^{ \frac{1}{6} + (\frac{-1}{3}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
10. \(a^{\frac{-5}{4}}.a^{-1}\\= a^{ \frac{-5}{4} + (-1) }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
11. \(y^{\frac{1}{4}}.y^{\frac{-5}{3}}\\= y^{ \frac{1}{4} + (\frac{-5}{3}) }= y^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{5} }}=\frac{1}{|y|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{2}|}\\---------------\)
12. \(y^{\frac{-4}{3}}.y^{\frac{5}{2}}\\= y^{ \frac{-4}{3} + \frac{5}{2} }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)