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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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