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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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