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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{5}{4}}.x^{1}\\= x^{ \frac{5}{4} + 1 }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
2. \(a^{\frac{1}{2}}.a^{\frac{-1}{4}}\\= a^{ \frac{1}{2} + (\frac{-1}{4}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
3. \(x^{\frac{-2}{3}}.x^{\frac{-1}{2}}\\= x^{ \frac{-2}{3} + (\frac{-1}{2}) }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
4. \(y^{1}.y^{\frac{5}{4}}\\= y^{ 1 + \frac{5}{4} }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
5. \(a^{\frac{1}{3}}.a^{\frac{3}{2}}\\= a^{ \frac{1}{3} + \frac{3}{2} }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
6. \(a^{\frac{-1}{3}}.a^{-1}\\= a^{ \frac{-1}{3} + (-1) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
7. \(x^{-2}.x^{\frac{-4}{5}}\\= x^{ -2 + (\frac{-4}{5}) }= x^{\frac{-14}{5}}\\=\frac{1}{\sqrt[5]{ x^{14} }}\\=\frac{1}{x^{2}.\sqrt[5]{ x^{4} }}=\frac{1}{x^{2}.\sqrt[5]{ x^{4} }} \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x^{3}}\\---------------\)
8. \(a^{\frac{-2}{5}}.a^{-1}\\= a^{ \frac{-2}{5} + (-1) }= a^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ a^{7} }}\\=\frac{1}{a.\sqrt[5]{ a^{2} }}=\frac{1}{a.\sqrt[5]{ a^{2} }} \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a^{2}}\\---------------\)
9. \(y^{-1}.y^{\frac{-1}{3}}\\= y^{ -1 + (\frac{-1}{3}) }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
10. \(y^{1}.y^{\frac{-1}{6}}\\= y^{ 1 + (\frac{-1}{6}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
11. \(a^{\frac{1}{2}}.a^{\frac{-5}{4}}\\= a^{ \frac{1}{2} + (\frac{-5}{4}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
12. \(q^{\frac{3}{5}}.q^{\frac{1}{6}}\\= q^{ \frac{3}{5} + \frac{1}{6} }= q^{\frac{23}{30}}\\=\sqrt[30]{ q^{23} }\\---------------\)