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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-5}{3}}.x^{\frac{-4}{5}}\\= x^{ \frac{-5}{3} + (\frac{-4}{5}) }= x^{\frac{-37}{15}}\\=\frac{1}{\sqrt[15]{ x^{37} }}\\=\frac{1}{x^{2}.\sqrt[15]{ x^{7} }}=\frac{1}{x^{2}.\sqrt[15]{ x^{7} }} \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x^{3}}\\---------------\)
2. \(a^{-1}.a^{-1}\\= a^{ -1 + (-1) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
3. \(x^{\frac{-1}{2}}.x^{\frac{3}{2}}\\= x^{ \frac{-1}{2} + \frac{3}{2} }= x^{1}\\\\---------------\)
4. \(x^{\frac{-5}{3}}.x^{\frac{-3}{5}}\\= x^{ \frac{-5}{3} + (\frac{-3}{5}) }= x^{\frac{-34}{15}}\\=\frac{1}{\sqrt[15]{ x^{34} }}\\=\frac{1}{x^{2}.\sqrt[15]{ x^{4} }}=\frac{1}{x^{2}.\sqrt[15]{ x^{4} }} \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x^{3}}\\---------------\)
5. \(a^{\frac{5}{3}}.a^{\frac{1}{2}}\\= a^{ \frac{5}{3} + \frac{1}{2} }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
6. \(x^{\frac{-1}{2}}.x^{\frac{-5}{4}}\\= x^{ \frac{-1}{2} + (\frac{-5}{4}) }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
7. \(q^{\frac{-5}{4}}.q^{-1}\\= q^{ \frac{-5}{4} + (-1) }= q^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ q^{9} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q }}=\frac{1}{|q^{2}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{3}|}\\---------------\)
8. \(x^{\frac{5}{6}}.x^{\frac{-2}{3}}\\= x^{ \frac{5}{6} + (\frac{-2}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
9. \(a^{\frac{1}{3}}.a^{-2}\\= a^{ \frac{1}{3} + (-2) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
10. \(x^{\frac{3}{2}}.x^{\frac{-2}{3}}\\= x^{ \frac{3}{2} + (\frac{-2}{3}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
11. \(a^{\frac{1}{2}}.a^{\frac{2}{3}}\\= a^{ \frac{1}{2} + \frac{2}{3} }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
12. \(q^{\frac{-1}{5}}.q^{\frac{-1}{4}}\\= q^{ \frac{-1}{5} + (\frac{-1}{4}) }= q^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ q^{9} }}=\frac{1}{\sqrt[20]{ q^{9} }}. \color{purple}{\frac{\sqrt[20]{ q^{11} }}{\sqrt[20]{ q^{11} }}} \\=\frac{\sqrt[20]{ q^{11} }}{|q|}\\---------------\)