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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(a^{-2}.a^{\frac{5}{6}}\\= a^{ -2 + \frac{5}{6} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
2. \(a^{\frac{-3}{2}}.a^{\frac{-2}{5}}\\= a^{ \frac{-3}{2} + (\frac{-2}{5}) }= a^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ a^{19} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{9} }}=\frac{1}{|a|.\sqrt[10]{ a^{9} }} \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a^{2}|}\\---------------\)
3. \(q^{-1}.q^{\frac{-4}{3}}\\= q^{ -1 + (\frac{-4}{3}) }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
4. \(x^{\frac{4}{3}}.x^{-1}\\= x^{ \frac{4}{3} + (-1) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
5. \(y^{\frac{2}{3}}.y^{1}\\= y^{ \frac{2}{3} + 1 }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
6. \(q^{-1}.q^{\frac{3}{2}}\\= q^{ -1 + \frac{3}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(a^{\frac{-1}{3}}.a^{\frac{-1}{5}}\\= a^{ \frac{-1}{3} + (\frac{-1}{5}) }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
8. \(y^{\frac{-3}{5}}.y^{-1}\\= y^{ \frac{-3}{5} + (-1) }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
9. \(x^{\frac{1}{3}}.x^{\frac{-2}{5}}\\= x^{ \frac{1}{3} + (\frac{-2}{5}) }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
10. \(y^{\frac{1}{3}}.y^{2}\\= y^{ \frac{1}{3} + 2 }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
11. \(y^{\frac{4}{3}}.y^{\frac{4}{3}}\\= y^{ \frac{4}{3} + \frac{4}{3} }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
12. \(y^{\frac{2}{3}}.y^{\frac{1}{3}}\\= y^{ \frac{2}{3} + \frac{1}{3} }= y^{1}\\\\---------------\)