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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-1}{4}}.x^{\frac{5}{2}}\\= x^{ \frac{-1}{4} + \frac{5}{2} }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
2. \(x^{\frac{1}{4}}.x^{-1}\\= x^{ \frac{1}{4} + (-1) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
3. \(x^{\frac{1}{3}}.x^{\frac{3}{2}}\\= x^{ \frac{1}{3} + \frac{3}{2} }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
4. \(y^{\frac{-5}{3}}.y^{\frac{1}{2}}\\= y^{ \frac{-5}{3} + \frac{1}{2} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
5. \(x^{\frac{4}{5}}.x^{\frac{-1}{2}}\\= x^{ \frac{4}{5} + (\frac{-1}{2}) }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
6. \(x^{\frac{5}{4}}.x^{\frac{-1}{6}}\\= x^{ \frac{5}{4} + (\frac{-1}{6}) }= x^{\frac{13}{12}}\\=\sqrt[12]{ x^{13} }=|x|.\sqrt[12]{ x }\\---------------\)
7. \(y^{\frac{-2}{3}}.y^{-1}\\= y^{ \frac{-2}{3} + (-1) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
8. \(x^{1}.x^{\frac{1}{4}}\\= x^{ 1 + \frac{1}{4} }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
9. \(y^{\frac{5}{2}}.y^{\frac{-5}{6}}\\= y^{ \frac{5}{2} + (\frac{-5}{6}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
10. \(a^{\frac{4}{5}}.a^{\frac{4}{3}}\\= a^{ \frac{4}{5} + \frac{4}{3} }= a^{\frac{32}{15}}\\=\sqrt[15]{ a^{32} }=a^{2}.\sqrt[15]{ a^{2} }\\---------------\)
11. \(a^{-1}.a^{-1}\\= a^{ -1 + (-1) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
12. \(q^{\frac{-2}{5}}.q^{\frac{1}{2}}\\= q^{ \frac{-2}{5} + \frac{1}{2} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)