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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{2}.x^{\frac{-4}{5}}\\= x^{ 2 + (\frac{-4}{5}) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
2. \(x^{\frac{-4}{5}}.x^{\frac{5}{6}}\\= x^{ \frac{-4}{5} + \frac{5}{6} }= x^{\frac{1}{30}}\\=\sqrt[30]{ x }\\---------------\)
3. \(q^{\frac{3}{5}}.q^{1}\\= q^{ \frac{3}{5} + 1 }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
4. \(a^{\frac{2}{3}}.a^{1}\\= a^{ \frac{2}{3} + 1 }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
5. \(q^{\frac{-4}{5}}.q^{\frac{-5}{2}}\\= q^{ \frac{-4}{5} + (\frac{-5}{2}) }= q^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ q^{33} }}\\=\frac{1}{|q^{3}|.\sqrt[10]{ q^{3} }}=\frac{1}{|q^{3}|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{4}|}\\---------------\)
6. \(a^{\frac{5}{6}}.a^{\frac{-3}{4}}\\= a^{ \frac{5}{6} + (\frac{-3}{4}) }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
7. \(q^{\frac{1}{5}}.q^{\frac{-5}{2}}\\= q^{ \frac{1}{5} + (\frac{-5}{2}) }= q^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ q^{23} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }}=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{3}|}\\---------------\)
8. \(y^{\frac{-1}{2}}.y^{\frac{-1}{3}}\\= y^{ \frac{-1}{2} + (\frac{-1}{3}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
9. \(y^{\frac{-1}{2}}.y^{-2}\\= y^{ \frac{-1}{2} + (-2) }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
10. \(q^{\frac{-1}{2}}.q^{\frac{5}{2}}\\= q^{ \frac{-1}{2} + \frac{5}{2} }= q^{2}\\\\---------------\)
11. \(q^{\frac{-4}{5}}.q^{\frac{-1}{5}}\\= q^{ \frac{-4}{5} + (\frac{-1}{5}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
12. \(x^{\frac{1}{3}}.x^{\frac{2}{3}}\\= x^{ \frac{1}{3} + \frac{2}{3} }= x^{1}\\\\---------------\)