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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{2}{5}}.y^{1}\\= y^{ \frac{2}{5} + 1 }= y^{\frac{7}{5}}\\=\sqrt[5]{ y^{7} }=y.\sqrt[5]{ y^{2} }\\---------------\)
2. \(a^{\frac{5}{3}}.a^{\frac{1}{5}}\\= a^{ \frac{5}{3} + \frac{1}{5} }= a^{\frac{28}{15}}\\=\sqrt[15]{ a^{28} }=a.\sqrt[15]{ a^{13} }\\---------------\)
3. \(x^{\frac{4}{5}}.x^{\frac{-5}{4}}\\= x^{ \frac{4}{5} + (\frac{-5}{4}) }= x^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ x^{9} }}=\frac{1}{\sqrt[20]{ x^{9} }}. \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x|}\\---------------\)
4. \(y^{\frac{1}{4}}.y^{\frac{1}{3}}\\= y^{ \frac{1}{4} + \frac{1}{3} }= y^{\frac{7}{12}}\\=\sqrt[12]{ y^{7} }\\---------------\)
5. \(x^{1}.x^{\frac{-4}{5}}\\= x^{ 1 + (\frac{-4}{5}) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
6. \(x^{\frac{-1}{2}}.x^{\frac{4}{5}}\\= x^{ \frac{-1}{2} + \frac{4}{5} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
7. \(a^{\frac{1}{6}}.a^{\frac{1}{2}}\\= a^{ \frac{1}{6} + \frac{1}{2} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
8. \(a^{-1}.a^{\frac{-1}{5}}\\= a^{ -1 + (\frac{-1}{5}) }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)
9. \(q^{\frac{1}{5}}.q^{-1}\\= q^{ \frac{1}{5} + (-1) }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
10. \(a^{-1}.a^{\frac{-1}{2}}\\= a^{ -1 + (\frac{-1}{2}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
11. \(y^{\frac{5}{2}}.y^{-1}\\= y^{ \frac{5}{2} + (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
12. \(q^{-2}.q^{1}\\= q^{ -2 + 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)