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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(a^{\frac{5}{6}}.a^{\frac{2}{3}}\\= a^{ \frac{5}{6} + \frac{2}{3} }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
2. \(x^{\frac{3}{5}}.x^{\frac{-2}{3}}\\= x^{ \frac{3}{5} + (\frac{-2}{3}) }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
3. \(a^{\frac{2}{3}}.a^{\frac{-2}{5}}\\= a^{ \frac{2}{3} + (\frac{-2}{5}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
4. \(x^{\frac{-2}{3}}.x^{\frac{-1}{2}}\\= x^{ \frac{-2}{3} + (\frac{-1}{2}) }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
5. \(a^{\frac{-5}{3}}.a^{\frac{-2}{5}}\\= a^{ \frac{-5}{3} + (\frac{-2}{5}) }= a^{\frac{-31}{15}}\\=\frac{1}{\sqrt[15]{ a^{31} }}\\=\frac{1}{a^{2}.\sqrt[15]{ a }}=\frac{1}{a^{2}.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{3}}\\---------------\)
6. \(q^{\frac{-1}{2}}.q^{\frac{-4}{5}}\\= q^{ \frac{-1}{2} + (\frac{-4}{5}) }= q^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{3} }}=\frac{1}{|q|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{2}|}\\---------------\)
7. \(q^{\frac{5}{2}}.q^{\frac{-2}{3}}\\= q^{ \frac{5}{2} + (\frac{-2}{3}) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
8. \(y^{-1}.y^{\frac{-3}{4}}\\= y^{ -1 + (\frac{-3}{4}) }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
9. \(a^{\frac{1}{2}}.a^{-2}\\= a^{ \frac{1}{2} + (-2) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
10. \(a^{\frac{-2}{3}}.a^{\frac{5}{4}}\\= a^{ \frac{-2}{3} + \frac{5}{4} }= a^{\frac{7}{12}}\\=\sqrt[12]{ a^{7} }\\---------------\)
11. \(a^{-1}.a^{\frac{4}{5}}\\= a^{ -1 + \frac{4}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
12. \(y^{-1}.y^{\frac{-1}{2}}\\= y^{ -1 + (\frac{-1}{2}) }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)