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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-1}{4}}.x^{\frac{2}{5}}\\= x^{ \frac{-1}{4} + \frac{2}{5} }= x^{\frac{3}{20}}\\=\sqrt[20]{ x^{3} }\\---------------\)
2. \(x^{\frac{-1}{6}}.x^{\frac{-5}{4}}\\= x^{ \frac{-1}{6} + (\frac{-5}{4}) }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
3. \(x^{\frac{-2}{5}}.x^{\frac{-3}{2}}\\= x^{ \frac{-2}{5} + (\frac{-3}{2}) }= x^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ x^{19} }}\\=\frac{1}{|x|.\sqrt[10]{ x^{9} }}=\frac{1}{|x|.\sqrt[10]{ x^{9} }} \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x^{2}|}\\---------------\)
4. \(q^{\frac{4}{3}}.q^{2}\\= q^{ \frac{4}{3} + 2 }= q^{\frac{10}{3}}\\=\sqrt[3]{ q^{10} }=q^{3}.\sqrt[3]{ q }\\---------------\)
5. \(x^{\frac{1}{2}}.x^{1}\\= x^{ \frac{1}{2} + 1 }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
6. \(a^{1}.a^{\frac{-1}{2}}\\= a^{ 1 + (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
7. \(x^{\frac{1}{2}}.x^{\frac{-5}{2}}\\= x^{ \frac{1}{2} + (\frac{-5}{2}) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
8. \(a^{-2}.a^{\frac{-4}{3}}\\= a^{ -2 + (\frac{-4}{3}) }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)
9. \(y^{\frac{-3}{4}}.y^{\frac{-3}{2}}\\= y^{ \frac{-3}{4} + (\frac{-3}{2}) }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
10. \(a^{\frac{-3}{5}}.a^{\frac{3}{2}}\\= a^{ \frac{-3}{5} + \frac{3}{2} }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
11. \(a^{-1}.a^{\frac{-1}{6}}\\= a^{ -1 + (\frac{-1}{6}) }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
12. \(a^{\frac{1}{2}}.a^{-1}\\= a^{ \frac{1}{2} + (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)