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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(a^{\frac{-3}{5}}.a^{\frac{-5}{6}}\\= a^{ \frac{-3}{5} + (\frac{-5}{6}) }= a^{\frac{-43}{30}}\\=\frac{1}{\sqrt[30]{ a^{43} }}\\=\frac{1}{|a|.\sqrt[30]{ a^{13} }}=\frac{1}{|a|.\sqrt[30]{ a^{13} }} \color{purple}{\frac{\sqrt[30]{ a^{17} }}{\sqrt[30]{ a^{17} }}} \\=\frac{\sqrt[30]{ a^{17} }}{|a^{2}|}\\---------------\)
2. \(y^{\frac{-1}{2}}.y^{\frac{2}{3}}\\= y^{ \frac{-1}{2} + \frac{2}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
3. \(q^{\frac{-1}{5}}.q^{-1}\\= q^{ \frac{-1}{5} + (-1) }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
4. \(x^{\frac{1}{2}}.x^{\frac{-3}{4}}\\= x^{ \frac{1}{2} + (\frac{-3}{4}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
5. \(q^{1}.q^{\frac{-4}{3}}\\= q^{ 1 + (\frac{-4}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
6. \(q^{\frac{4}{5}}.q^{-1}\\= q^{ \frac{4}{5} + (-1) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
7. \(x^{\frac{-1}{3}}.x^{\frac{3}{4}}\\= x^{ \frac{-1}{3} + \frac{3}{4} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
8. \(q^{\frac{2}{3}}.q^{\frac{-2}{3}}\\= q^{ \frac{2}{3} + (\frac{-2}{3}) }= q^{0}\\=1\\---------------\)
9. \(x^{\frac{1}{2}}.x^{\frac{1}{2}}\\= x^{ \frac{1}{2} + \frac{1}{2} }= x^{1}\\\\---------------\)
10. \(x^{\frac{-1}{3}}.x^{1}\\= x^{ \frac{-1}{3} + 1 }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
11. \(a^{\frac{-1}{3}}.a^{\frac{5}{4}}\\= a^{ \frac{-1}{3} + \frac{5}{4} }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
12. \(y^{1}.y^{\frac{-2}{5}}\\= y^{ 1 + (\frac{-2}{5}) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)