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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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