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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(a^{\frac{4}{3}}.a^{\frac{-1}{6}}\\= a^{ \frac{4}{3} + (\frac{-1}{6}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
2. \(a^{\frac{-1}{2}}.a^{\frac{-1}{2}}\\= a^{ \frac{-1}{2} + (\frac{-1}{2}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
3. \(y^{1}.y^{1}\\= y^{ 1 + 1 }= y^{2}\\\\---------------\)
4. \(a^{\frac{2}{3}}.a^{\frac{-5}{4}}\\= a^{ \frac{2}{3} + (\frac{-5}{4}) }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
5. \(a^{\frac{-5}{4}}.a^{\frac{-1}{5}}\\= a^{ \frac{-5}{4} + (\frac{-1}{5}) }= a^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ a^{29} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{9} }}=\frac{1}{|a|.\sqrt[20]{ a^{9} }} \color{purple}{\frac{\sqrt[20]{ a^{11} }}{\sqrt[20]{ a^{11} }}} \\=\frac{\sqrt[20]{ a^{11} }}{|a^{2}|}\\---------------\)
6. \(a^{\frac{1}{4}}.a^{\frac{2}{3}}\\= a^{ \frac{1}{4} + \frac{2}{3} }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
7. \(x^{\frac{1}{3}}.x^{\frac{-3}{5}}\\= x^{ \frac{1}{3} + (\frac{-3}{5}) }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
8. \(y^{2}.y^{\frac{-1}{3}}\\= y^{ 2 + (\frac{-1}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
9. \(y^{\frac{-5}{6}}.y^{\frac{2}{3}}\\= y^{ \frac{-5}{6} + \frac{2}{3} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
10. \(q^{\frac{-2}{3}}.q^{\frac{-1}{4}}\\= q^{ \frac{-2}{3} + (\frac{-1}{4}) }= q^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ q^{11} }}=\frac{1}{\sqrt[12]{ q^{11} }}. \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q|}\\---------------\)
11. \(q^{\frac{4}{3}}.q^{\frac{3}{4}}\\= q^{ \frac{4}{3} + \frac{3}{4} }= q^{\frac{25}{12}}\\=\sqrt[12]{ q^{25} }=|q^{2}|.\sqrt[12]{ q }\\---------------\)
12. \(y^{\frac{1}{2}}.y^{\frac{5}{4}}\\= y^{ \frac{1}{2} + \frac{5}{4} }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)