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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{-1}{5}}.y^{-1}\\= y^{ \frac{-1}{5} + (-1) }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
2. \(a^{1}.a^{\frac{-1}{2}}\\= a^{ 1 + (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
3. \(x^{1}.x^{-1}\\= x^{ 1 + (-1) }= x^{0}\\=1\\---------------\)
4. \(q^{\frac{-1}{6}}.q^{\frac{2}{3}}\\= q^{ \frac{-1}{6} + \frac{2}{3} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
5. \(x^{\frac{-1}{2}}.x^{\frac{3}{4}}\\= x^{ \frac{-1}{2} + \frac{3}{4} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
6. \(a^{\frac{3}{5}}.a^{\frac{1}{3}}\\= a^{ \frac{3}{5} + \frac{1}{3} }= a^{\frac{14}{15}}\\=\sqrt[15]{ a^{14} }\\---------------\)
7. \(x^{1}.x^{\frac{-5}{4}}\\= x^{ 1 + (\frac{-5}{4}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
8. \(q^{\frac{-1}{6}}.q^{\frac{1}{2}}\\= q^{ \frac{-1}{6} + \frac{1}{2} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
9. \(y^{\frac{3}{4}}.y^{\frac{-3}{2}}\\= y^{ \frac{3}{4} + (\frac{-3}{2}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
10. \(q^{-1}.q^{-1}\\= q^{ -1 + (-1) }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
11. \(x^{-1}.x^{\frac{-1}{3}}\\= x^{ -1 + (\frac{-1}{3}) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
12. \(y^{\frac{3}{2}}.y^{-2}\\= y^{ \frac{3}{2} + (-2) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)