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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(a^{\frac{1}{3}}.a^{\frac{-2}{3}}\\= a^{ \frac{1}{3} + (\frac{-2}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(q^{\frac{5}{3}}.q^{\frac{5}{6}}\\= q^{ \frac{5}{3} + \frac{5}{6} }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
3. \(a^{\frac{2}{3}}.a^{1}\\= a^{ \frac{2}{3} + 1 }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
4. \(q^{\frac{3}{4}}.q^{\frac{-1}{3}}\\= q^{ \frac{3}{4} + (\frac{-1}{3}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
5. \(a^{-1}.a^{\frac{-1}{5}}\\= a^{ -1 + (\frac{-1}{5}) }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)
6. \(q^{\frac{5}{3}}.q^{\frac{1}{2}}\\= q^{ \frac{5}{3} + \frac{1}{2} }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
7. \(y^{1}.y^{-1}\\= y^{ 1 + (-1) }= y^{0}\\=1\\---------------\)
8. \(y^{\frac{-1}{2}}.y^{\frac{-1}{3}}\\= y^{ \frac{-1}{2} + (\frac{-1}{3}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
9. \(y^{\frac{-3}{5}}.y^{\frac{-3}{2}}\\= y^{ \frac{-3}{5} + (\frac{-3}{2}) }= y^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ y^{21} }}\\=\frac{1}{|y^{2}|.\sqrt[10]{ y }}=\frac{1}{|y^{2}|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{3}|}\\---------------\)
10. \(y^{\frac{1}{4}}.y^{\frac{2}{3}}\\= y^{ \frac{1}{4} + \frac{2}{3} }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
11. \(a^{\frac{2}{3}}.a^{\frac{1}{6}}\\= a^{ \frac{2}{3} + \frac{1}{6} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
12. \(x^{\frac{2}{5}}.x^{\frac{2}{5}}\\= x^{ \frac{2}{5} + \frac{2}{5} }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)