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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{-1}.y^{\frac{-2}{3}}\\= y^{ -1 + (\frac{-2}{3}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
2. \(q^{\frac{3}{5}}.q^{\frac{-5}{4}}\\= q^{ \frac{3}{5} + (\frac{-5}{4}) }= q^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ q^{13} }}=\frac{1}{\sqrt[20]{ q^{13} }}. \color{purple}{\frac{\sqrt[20]{ q^{7} }}{\sqrt[20]{ q^{7} }}} \\=\frac{\sqrt[20]{ q^{7} }}{|q|}\\---------------\)
3. \(a^{\frac{-5}{4}}.a^{\frac{4}{5}}\\= a^{ \frac{-5}{4} + \frac{4}{5} }= a^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ a^{9} }}=\frac{1}{\sqrt[20]{ a^{9} }}. \color{purple}{\frac{\sqrt[20]{ a^{11} }}{\sqrt[20]{ a^{11} }}} \\=\frac{\sqrt[20]{ a^{11} }}{|a|}\\---------------\)
4. \(q^{\frac{-2}{5}}.q^{\frac{5}{2}}\\= q^{ \frac{-2}{5} + \frac{5}{2} }= q^{\frac{21}{10}}\\=\sqrt[10]{ q^{21} }=|q^{2}|.\sqrt[10]{ q }\\---------------\)
5. \(y^{\frac{-5}{2}}.y^{\frac{1}{2}}\\= y^{ \frac{-5}{2} + \frac{1}{2} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
6. \(a^{\frac{1}{6}}.a^{\frac{5}{4}}\\= a^{ \frac{1}{6} + \frac{5}{4} }= a^{\frac{17}{12}}\\=\sqrt[12]{ a^{17} }=|a|.\sqrt[12]{ a^{5} }\\---------------\)
7. \(a^{\frac{1}{5}}.a^{\frac{-1}{3}}\\= a^{ \frac{1}{5} + (\frac{-1}{3}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
8. \(a^{\frac{-3}{5}}.a^{\frac{-1}{4}}\\= a^{ \frac{-3}{5} + (\frac{-1}{4}) }= a^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ a^{17} }}=\frac{1}{\sqrt[20]{ a^{17} }}. \color{purple}{\frac{\sqrt[20]{ a^{3} }}{\sqrt[20]{ a^{3} }}} \\=\frac{\sqrt[20]{ a^{3} }}{|a|}\\---------------\)
9. \(x^{\frac{-3}{5}}.x^{\frac{1}{2}}\\= x^{ \frac{-3}{5} + \frac{1}{2} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
10. \(x^{\frac{4}{5}}.x^{\frac{-4}{3}}\\= x^{ \frac{4}{5} + (\frac{-4}{3}) }= x^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ x^{8} }}=\frac{1}{\sqrt[15]{ x^{8} }}. \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x}\\---------------\)
11. \(x^{\frac{-5}{3}}.x^{\frac{-1}{5}}\\= x^{ \frac{-5}{3} + (\frac{-1}{5}) }= x^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ x^{28} }}\\=\frac{1}{x.\sqrt[15]{ x^{13} }}=\frac{1}{x.\sqrt[15]{ x^{13} }} \color{purple}{\frac{\sqrt[15]{ x^{2} }}{\sqrt[15]{ x^{2} }}} \\=\frac{\sqrt[15]{ x^{2} }}{x^{2}}\\---------------\)
12. \(q^{1}.q^{-1}\\= q^{ 1 + (-1) }= q^{0}\\=1\\---------------\)