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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-3}{2}}.x^{1}\\= x^{ \frac{-3}{2} + 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
2. \(a^{1}.a^{\frac{-1}{2}}\\= a^{ 1 + (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
3. \(y^{\frac{-1}{2}}.y^{\frac{-1}{6}}\\= y^{ \frac{-1}{2} + (\frac{-1}{6}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
4. \(x^{\frac{-1}{2}}.x^{\frac{-2}{3}}\\= x^{ \frac{-1}{2} + (\frac{-2}{3}) }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
5. \(a^{\frac{1}{2}}.a^{\frac{-5}{6}}\\= a^{ \frac{1}{2} + (\frac{-5}{6}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
6. \(x^{-2}.x^{\frac{5}{2}}\\= x^{ -2 + \frac{5}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
7. \(y^{\frac{-1}{5}}.y^{\frac{2}{3}}\\= y^{ \frac{-1}{5} + \frac{2}{3} }= y^{\frac{7}{15}}\\=\sqrt[15]{ y^{7} }\\---------------\)
8. \(a^{\frac{-1}{2}}.a^{\frac{1}{4}}\\= a^{ \frac{-1}{2} + \frac{1}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
9. \(x^{\frac{1}{5}}.x^{-1}\\= x^{ \frac{1}{5} + (-1) }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
10. \(x^{\frac{-1}{2}}.x^{\frac{-1}{4}}\\= x^{ \frac{-1}{2} + (\frac{-1}{4}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
11. \(q^{\frac{-1}{3}}.q^{\frac{-2}{5}}\\= q^{ \frac{-1}{3} + (\frac{-2}{5}) }= q^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ q^{11} }}=\frac{1}{\sqrt[15]{ q^{11} }}. \color{purple}{\frac{\sqrt[15]{ q^{4} }}{\sqrt[15]{ q^{4} }}} \\=\frac{\sqrt[15]{ q^{4} }}{q}\\---------------\)
12. \(a^{\frac{-1}{3}}.a^{-1}\\= a^{ \frac{-1}{3} + (-1) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)