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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{1}.x^{\frac{4}{5}}\\= x^{ 1 + \frac{4}{5} }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
2. \(a^{1}.a^{\frac{-1}{2}}\\= a^{ 1 + (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
3. \(q^{\frac{2}{3}}.q^{\frac{5}{2}}\\= q^{ \frac{2}{3} + \frac{5}{2} }= q^{\frac{19}{6}}\\=\sqrt[6]{ q^{19} }=|q^{3}|.\sqrt[6]{ q }\\---------------\)
4. \(y^{\frac{-3}{2}}.y^{\frac{1}{6}}\\= y^{ \frac{-3}{2} + \frac{1}{6} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
5. \(q^{\frac{-2}{3}}.q^{\frac{-5}{4}}\\= q^{ \frac{-2}{3} + (\frac{-5}{4}) }= q^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ q^{23} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{11} }}=\frac{1}{|q|.\sqrt[12]{ q^{11} }} \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q^{2}|}\\---------------\)
6. \(a^{\frac{-5}{6}}.a^{1}\\= a^{ \frac{-5}{6} + 1 }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
7. \(x^{\frac{1}{5}}.x^{\frac{3}{4}}\\= x^{ \frac{1}{5} + \frac{3}{4} }= x^{\frac{19}{20}}\\=\sqrt[20]{ x^{19} }\\---------------\)
8. \(a^{\frac{-4}{3}}.a^{\frac{5}{6}}\\= a^{ \frac{-4}{3} + \frac{5}{6} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
9. \(q^{-1}.q^{2}\\= q^{ -1 + 2 }= q^{1}\\\\---------------\)
10. \(a^{\frac{-1}{2}}.a^{1}\\= a^{ \frac{-1}{2} + 1 }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
11. \(x^{\frac{-5}{6}}.x^{\frac{1}{2}}\\= x^{ \frac{-5}{6} + \frac{1}{2} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
12. \(x^{\frac{2}{5}}.x^{\frac{-5}{2}}\\= x^{ \frac{2}{5} + (\frac{-5}{2}) }= x^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ x^{21} }}\\=\frac{1}{|x^{2}|.\sqrt[10]{ x }}=\frac{1}{|x^{2}|.\sqrt[10]{ x }} \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x^{3}|}\\---------------\)