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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{5}{4}}.y^{\frac{-5}{2}}\\= y^{ \frac{5}{4} + (\frac{-5}{2}) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
2. \(a^{\frac{-1}{2}}.a^{\frac{-1}{4}}\\= a^{ \frac{-1}{2} + (\frac{-1}{4}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
3. \(y^{\frac{4}{3}}.y^{\frac{-2}{5}}\\= y^{ \frac{4}{3} + (\frac{-2}{5}) }= y^{\frac{14}{15}}\\=\sqrt[15]{ y^{14} }\\---------------\)
4. \(q^{\frac{5}{6}}.q^{\frac{5}{6}}\\= q^{ \frac{5}{6} + \frac{5}{6} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
5. \(y^{\frac{-1}{5}}.y^{\frac{5}{3}}\\= y^{ \frac{-1}{5} + \frac{5}{3} }= y^{\frac{22}{15}}\\=\sqrt[15]{ y^{22} }=y.\sqrt[15]{ y^{7} }\\---------------\)
6. \(a^{\frac{-3}{2}}.a^{\frac{4}{5}}\\= a^{ \frac{-3}{2} + \frac{4}{5} }= a^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ a^{7} }}=\frac{1}{\sqrt[10]{ a^{7} }}. \color{purple}{\frac{\sqrt[10]{ a^{3} }}{\sqrt[10]{ a^{3} }}} \\=\frac{\sqrt[10]{ a^{3} }}{|a|}\\---------------\)
7. \(q^{2}.q^{\frac{1}{3}}\\= q^{ 2 + \frac{1}{3} }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
8. \(x^{\frac{3}{2}}.x^{\frac{-1}{5}}\\= x^{ \frac{3}{2} + (\frac{-1}{5}) }= x^{\frac{13}{10}}\\=\sqrt[10]{ x^{13} }=|x|.\sqrt[10]{ x^{3} }\\---------------\)
9. \(q^{1}.q^{\frac{-1}{2}}\\= q^{ 1 + (\frac{-1}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(x^{\frac{1}{2}}.x^{-2}\\= x^{ \frac{1}{2} + (-2) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
11. \(q^{\frac{-1}{6}}.q^{-1}\\= q^{ \frac{-1}{6} + (-1) }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
12. \(y^{\frac{-1}{2}}.y^{\frac{-3}{2}}\\= y^{ \frac{-1}{2} + (\frac{-3}{2}) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)