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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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