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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{3}{2}}.q^{1}\\= q^{ \frac{3}{2} + 1 }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
2. \(y^{\frac{-5}{4}}.y^{\frac{-1}{5}}\\= y^{ \frac{-5}{4} + (\frac{-1}{5}) }= y^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ y^{29} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{9} }}=\frac{1}{|y|.\sqrt[20]{ y^{9} }} \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y^{2}|}\\---------------\)
3. \(x^{\frac{3}{2}}.x^{\frac{1}{5}}\\= x^{ \frac{3}{2} + \frac{1}{5} }= x^{\frac{17}{10}}\\=\sqrt[10]{ x^{17} }=|x|.\sqrt[10]{ x^{7} }\\---------------\)
4. \(y^{\frac{-3}{2}}.y^{\frac{-2}{5}}\\= y^{ \frac{-3}{2} + (\frac{-2}{5}) }= y^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{9} }}=\frac{1}{|y|.\sqrt[10]{ y^{9} }} \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y^{2}|}\\---------------\)
5. \(a^{\frac{1}{2}}.a^{-1}\\= a^{ \frac{1}{2} + (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
6. \(x^{\frac{4}{5}}.x^{\frac{-5}{3}}\\= x^{ \frac{4}{5} + (\frac{-5}{3}) }= x^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ x^{13} }}=\frac{1}{\sqrt[15]{ x^{13} }}. \color{purple}{\frac{\sqrt[15]{ x^{2} }}{\sqrt[15]{ x^{2} }}} \\=\frac{\sqrt[15]{ x^{2} }}{x}\\---------------\)
7. \(q^{\frac{-3}{5}}.q^{\frac{4}{3}}\\= q^{ \frac{-3}{5} + \frac{4}{3} }= q^{\frac{11}{15}}\\=\sqrt[15]{ q^{11} }\\---------------\)
8. \(q^{\frac{-1}{5}}.q^{-2}\\= q^{ \frac{-1}{5} + (-2) }= q^{\frac{-11}{5}}\\=\frac{1}{\sqrt[5]{ q^{11} }}\\=\frac{1}{q^{2}.\sqrt[5]{ q }}=\frac{1}{q^{2}.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{3}}\\---------------\)
9. \(a^{\frac{1}{2}}.a^{2}\\= a^{ \frac{1}{2} + 2 }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
10. \(y^{\frac{3}{4}}.y^{\frac{1}{5}}\\= y^{ \frac{3}{4} + \frac{1}{5} }= y^{\frac{19}{20}}\\=\sqrt[20]{ y^{19} }\\---------------\)
11. \(y^{\frac{1}{6}}.y^{1}\\= y^{ \frac{1}{6} + 1 }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
12. \(y^{\frac{4}{5}}.y^{\frac{-2}{3}}\\= y^{ \frac{4}{5} + (\frac{-2}{3}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)