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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{1}{4}}.x^{\frac{3}{5}}\\= x^{ \frac{1}{4} + \frac{3}{5} }= x^{\frac{17}{20}}\\=\sqrt[20]{ x^{17} }\\---------------\)
2. \(x^{1}.x^{\frac{3}{2}}\\= x^{ 1 + \frac{3}{2} }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
3. \(y^{2}.y^{\frac{1}{2}}\\= y^{ 2 + \frac{1}{2} }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
4. \(a^{\frac{5}{6}}.a^{\frac{1}{5}}\\= a^{ \frac{5}{6} + \frac{1}{5} }= a^{\frac{31}{30}}\\=\sqrt[30]{ a^{31} }=|a|.\sqrt[30]{ a }\\---------------\)
5. \(a^{\frac{-1}{5}}.a^{\frac{-5}{6}}\\= a^{ \frac{-1}{5} + (\frac{-5}{6}) }= a^{\frac{-31}{30}}\\=\frac{1}{\sqrt[30]{ a^{31} }}\\=\frac{1}{|a|.\sqrt[30]{ a }}=\frac{1}{|a|.\sqrt[30]{ a }} \color{purple}{\frac{\sqrt[30]{ a^{29} }}{\sqrt[30]{ a^{29} }}} \\=\frac{\sqrt[30]{ a^{29} }}{|a^{2}|}\\---------------\)
6. \(a^{\frac{-5}{3}}.a^{\frac{1}{3}}\\= a^{ \frac{-5}{3} + \frac{1}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
7. \(q^{\frac{5}{4}}.q^{\frac{-3}{4}}\\= q^{ \frac{5}{4} + (\frac{-3}{4}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
8. \(x^{\frac{5}{4}}.x^{\frac{2}{5}}\\= x^{ \frac{5}{4} + \frac{2}{5} }= x^{\frac{33}{20}}\\=\sqrt[20]{ x^{33} }=|x|.\sqrt[20]{ x^{13} }\\---------------\)
9. \(y^{\frac{-1}{2}}.y^{\frac{-3}{5}}\\= y^{ \frac{-1}{2} + (\frac{-3}{5}) }= y^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[10]{ y }}=\frac{1}{|y|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{2}|}\\---------------\)
10. \(q^{\frac{5}{6}}.q^{\frac{1}{3}}\\= q^{ \frac{5}{6} + \frac{1}{3} }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
11. \(x^{\frac{1}{2}}.x^{\frac{-3}{2}}\\= x^{ \frac{1}{2} + (\frac{-3}{2}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
12. \(x^{\frac{-1}{3}}.x^{\frac{-1}{3}}\\= x^{ \frac{-1}{3} + (\frac{-1}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)