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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{5}{4}}.x^{\frac{1}{2}}\\= x^{ \frac{5}{4} + \frac{1}{2} }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
2. \(y^{-1}.y^{-1}\\= y^{ -1 + (-1) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
3. \(a^{\frac{1}{4}}.a^{\frac{-4}{5}}\\= a^{ \frac{1}{4} + (\frac{-4}{5}) }= a^{\frac{-11}{20}}\\=\frac{1}{\sqrt[20]{ a^{11} }}=\frac{1}{\sqrt[20]{ a^{11} }}. \color{purple}{\frac{\sqrt[20]{ a^{9} }}{\sqrt[20]{ a^{9} }}} \\=\frac{\sqrt[20]{ a^{9} }}{|a|}\\---------------\)
4. \(y^{1}.y^{\frac{-1}{5}}\\= y^{ 1 + (\frac{-1}{5}) }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
5. \(a^{2}.a^{\frac{5}{3}}\\= a^{ 2 + \frac{5}{3} }= a^{\frac{11}{3}}\\=\sqrt[3]{ a^{11} }=a^{3}.\sqrt[3]{ a^{2} }\\---------------\)
6. \(y^{\frac{3}{2}}.y^{-1}\\= y^{ \frac{3}{2} + (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
7. \(y^{\frac{1}{3}}.y^{\frac{4}{3}}\\= y^{ \frac{1}{3} + \frac{4}{3} }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
8. \(y^{\frac{1}{3}}.y^{1}\\= y^{ \frac{1}{3} + 1 }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
9. \(x^{1}.x^{\frac{-1}{4}}\\= x^{ 1 + (\frac{-1}{4}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
10. \(x^{\frac{-1}{2}}.x^{-1}\\= x^{ \frac{-1}{2} + (-1) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
11. \(a^{\frac{-1}{2}}.a^{\frac{-1}{3}}\\= a^{ \frac{-1}{2} + (\frac{-1}{3}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
12. \(y^{1}.y^{\frac{4}{3}}\\= y^{ 1 + \frac{4}{3} }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)