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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{-4}{5}}.y^{\frac{2}{5}}\\= y^{ \frac{-4}{5} + \frac{2}{5} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
2. \(x^{\frac{-1}{2}}.x^{\frac{1}{3}}\\= x^{ \frac{-1}{2} + \frac{1}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
3. \(x^{-1}.x^{\frac{-1}{6}}\\= x^{ -1 + (\frac{-1}{6}) }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
4. \(x^{\frac{5}{2}}.x^{\frac{-1}{2}}\\= x^{ \frac{5}{2} + (\frac{-1}{2}) }= x^{2}\\\\---------------\)
5. \(q^{-1}.q^{\frac{-1}{3}}\\= q^{ -1 + (\frac{-1}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
6. \(a^{\frac{2}{3}}.a^{\frac{1}{6}}\\= a^{ \frac{2}{3} + \frac{1}{6} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
7. \(x^{\frac{-1}{2}}.x^{\frac{1}{6}}\\= x^{ \frac{-1}{2} + \frac{1}{6} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
8. \(a^{-1}.a^{\frac{-2}{3}}\\= a^{ -1 + (\frac{-2}{3}) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
9. \(a^{\frac{-2}{5}}.a^{\frac{-1}{2}}\\= a^{ \frac{-2}{5} + (\frac{-1}{2}) }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
10. \(x^{\frac{1}{4}}.x^{\frac{-2}{3}}\\= x^{ \frac{1}{4} + (\frac{-2}{3}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
11. \(y^{\frac{5}{4}}.y^{1}\\= y^{ \frac{5}{4} + 1 }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
12. \(y^{\frac{-1}{5}}.y^{\frac{5}{6}}\\= y^{ \frac{-1}{5} + \frac{5}{6} }= y^{\frac{19}{30}}\\=\sqrt[30]{ y^{19} }\\---------------\)