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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(a^{\frac{2}{3}}.a^{\frac{1}{3}}\\= a^{ \frac{2}{3} + \frac{1}{3} }= a^{1}\\\\---------------\)
2. \(y^{\frac{1}{3}}.y^{\frac{5}{3}}\\= y^{ \frac{1}{3} + \frac{5}{3} }= y^{2}\\\\---------------\)
3. \(y^{\frac{1}{2}}.y^{\frac{-5}{6}}\\= y^{ \frac{1}{2} + (\frac{-5}{6}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
4. \(y^{\frac{-2}{5}}.y^{\frac{-2}{3}}\\= y^{ \frac{-2}{5} + (\frac{-2}{3}) }= y^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ y^{16} }}\\=\frac{1}{y.\sqrt[15]{ y }}=\frac{1}{y.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{2}}\\---------------\)
5. \(y^{\frac{-1}{4}}.y^{\frac{1}{6}}\\= y^{ \frac{-1}{4} + \frac{1}{6} }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
6. \(x^{\frac{1}{2}}.x^{-1}\\= x^{ \frac{1}{2} + (-1) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
7. \(a^{\frac{-3}{4}}.a^{\frac{-1}{4}}\\= a^{ \frac{-3}{4} + (\frac{-1}{4}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
8. \(y^{-2}.y^{1}\\= y^{ -2 + 1 }= y^{-1}\\=\frac{1}{y}\\---------------\)
9. \(y^{\frac{1}{2}}.y^{\frac{1}{5}}\\= y^{ \frac{1}{2} + \frac{1}{5} }= y^{\frac{7}{10}}\\=\sqrt[10]{ y^{7} }\\---------------\)
10. \(a^{1}.a^{\frac{-1}{3}}\\= a^{ 1 + (\frac{-1}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
11. \(q^{\frac{5}{3}}.q^{\frac{-5}{2}}\\= q^{ \frac{5}{3} + (\frac{-5}{2}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
12. \(a^{\frac{2}{3}}.a^{\frac{4}{3}}\\= a^{ \frac{2}{3} + \frac{4}{3} }= a^{2}\\\\---------------\)