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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{1}{2}}.y^{1}\\= y^{ \frac{1}{2} + 1 }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
2. \(y^{\frac{-1}{3}}.y^{\frac{-4}{5}}\\= y^{ \frac{-1}{3} + (\frac{-4}{5}) }= y^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ y^{17} }}\\=\frac{1}{y.\sqrt[15]{ y^{2} }}=\frac{1}{y.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{2}}\\---------------\)
3. \(x^{\frac{-1}{3}}.x^{\frac{-3}{5}}\\= x^{ \frac{-1}{3} + (\frac{-3}{5}) }= x^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ x^{14} }}=\frac{1}{\sqrt[15]{ x^{14} }}. \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x}\\---------------\)
4. \(y^{\frac{-5}{3}}.y^{-2}\\= y^{ \frac{-5}{3} + (-2) }= y^{\frac{-11}{3}}\\=\frac{1}{\sqrt[3]{ y^{11} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{3}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{4}}\\---------------\)
5. \(x^{1}.x^{2}\\= x^{ 1 + 2 }= x^{3}\\\\---------------\)
6. \(x^{\frac{-2}{3}}.x^{\frac{1}{2}}\\= x^{ \frac{-2}{3} + \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
7. \(x^{\frac{5}{3}}.x^{-1}\\= x^{ \frac{5}{3} + (-1) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
8. \(q^{-2}.q^{1}\\= q^{ -2 + 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)
9. \(a^{\frac{5}{6}}.a^{-1}\\= a^{ \frac{5}{6} + (-1) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
10. \(q^{\frac{-4}{5}}.q^{\frac{3}{4}}\\= q^{ \frac{-4}{5} + \frac{3}{4} }= q^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ q }}=\frac{1}{\sqrt[20]{ q }}. \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q|}\\---------------\)
11. \(x^{\frac{5}{4}}.x^{\frac{2}{5}}\\= x^{ \frac{5}{4} + \frac{2}{5} }= x^{\frac{33}{20}}\\=\sqrt[20]{ x^{33} }=|x|.\sqrt[20]{ x^{13} }\\---------------\)
12. \(y^{2}.y^{\frac{1}{6}}\\= y^{ 2 + \frac{1}{6} }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)