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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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