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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{-1}{3}}.q^{\frac{2}{5}}\\= q^{ \frac{-1}{3} + \frac{2}{5} }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
2. \(a^{\frac{5}{4}}.a^{\frac{2}{3}}\\= a^{ \frac{5}{4} + \frac{2}{3} }= a^{\frac{23}{12}}\\=\sqrt[12]{ a^{23} }=|a|.\sqrt[12]{ a^{11} }\\---------------\)
3. \(q^{\frac{-4}{5}}.q^{-1}\\= q^{ \frac{-4}{5} + (-1) }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
4. \(y^{\frac{-1}{3}}.y^{\frac{-2}{3}}\\= y^{ \frac{-1}{3} + (\frac{-2}{3}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
5. \(a^{\frac{1}{3}}.a^{\frac{-5}{4}}\\= a^{ \frac{1}{3} + (\frac{-5}{4}) }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
6. \(a^{\frac{5}{2}}.a^{2}\\= a^{ \frac{5}{2} + 2 }= a^{\frac{9}{2}}\\= \sqrt{ a^{9} } =|a^{4}|. \sqrt{ a } \\---------------\)
7. \(y^{\frac{-1}{2}}.y^{\frac{2}{3}}\\= y^{ \frac{-1}{2} + \frac{2}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
8. \(a^{-1}.a^{\frac{-1}{2}}\\= a^{ -1 + (\frac{-1}{2}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
9. \(y^{\frac{3}{5}}.y^{\frac{5}{4}}\\= y^{ \frac{3}{5} + \frac{5}{4} }= y^{\frac{37}{20}}\\=\sqrt[20]{ y^{37} }=|y|.\sqrt[20]{ y^{17} }\\---------------\)
10. \(q^{-2}.q^{-2}\\= q^{ -2 + (-2) }= q^{-4}\\=\frac{1}{q^{4}}\\---------------\)
11. \(a^{\frac{-1}{6}}.a^{\frac{-1}{3}}\\= a^{ \frac{-1}{6} + (\frac{-1}{3}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
12. \(y^{\frac{3}{2}}.y^{\frac{-3}{5}}\\= y^{ \frac{3}{2} + (\frac{-3}{5}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)