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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{2}{3}}.q^{\frac{-4}{5}}\\= q^{ \frac{2}{3} + (\frac{-4}{5}) }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
2. \(a^{\frac{1}{4}}.a^{\frac{1}{3}}\\= a^{ \frac{1}{4} + \frac{1}{3} }= a^{\frac{7}{12}}\\=\sqrt[12]{ a^{7} }\\---------------\)
3. \(x^{\frac{-3}{5}}.x^{\frac{3}{5}}\\= x^{ \frac{-3}{5} + \frac{3}{5} }= x^{0}\\=1\\---------------\)
4. \(q^{\frac{4}{5}}.q^{\frac{1}{3}}\\= q^{ \frac{4}{5} + \frac{1}{3} }= q^{\frac{17}{15}}\\=\sqrt[15]{ q^{17} }=q.\sqrt[15]{ q^{2} }\\---------------\)
5. \(a^{\frac{1}{3}}.a^{\frac{-4}{3}}\\= a^{ \frac{1}{3} + (\frac{-4}{3}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
6. \(q^{\frac{-1}{4}}.q^{\frac{1}{2}}\\= q^{ \frac{-1}{4} + \frac{1}{2} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
7. \(y^{\frac{-2}{5}}.y^{\frac{5}{2}}\\= y^{ \frac{-2}{5} + \frac{5}{2} }= y^{\frac{21}{10}}\\=\sqrt[10]{ y^{21} }=|y^{2}|.\sqrt[10]{ y }\\---------------\)
8. \(x^{\frac{-5}{3}}.x^{\frac{5}{6}}\\= x^{ \frac{-5}{3} + \frac{5}{6} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
9. \(a^{\frac{1}{3}}.a^{\frac{-2}{5}}\\= a^{ \frac{1}{3} + (\frac{-2}{5}) }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
10. \(q^{-1}.q^{\frac{-5}{6}}\\= q^{ -1 + (\frac{-5}{6}) }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
11. \(q^{1}.q^{\frac{4}{5}}\\= q^{ 1 + \frac{4}{5} }= q^{\frac{9}{5}}\\=\sqrt[5]{ q^{9} }=q.\sqrt[5]{ q^{4} }\\---------------\)
12. \(x^{1}.x^{\frac{-1}{5}}\\= x^{ 1 + (\frac{-1}{5}) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)