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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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