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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{1}{2}}.y^{1}\\= y^{ \frac{1}{2} + 1 }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
2. \(x^{\frac{1}{2}}.x^{\frac{-1}{3}}\\= x^{ \frac{1}{2} + (\frac{-1}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
3. \(y^{\frac{-1}{2}}.y^{\frac{-1}{5}}\\= y^{ \frac{-1}{2} + (\frac{-1}{5}) }= y^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ y^{7} }}=\frac{1}{\sqrt[10]{ y^{7} }}. \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y|}\\---------------\)
4. \(a^{\frac{-2}{3}}.a^{\frac{-4}{5}}\\= a^{ \frac{-2}{3} + (\frac{-4}{5}) }= a^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ a^{22} }}\\=\frac{1}{a.\sqrt[15]{ a^{7} }}=\frac{1}{a.\sqrt[15]{ a^{7} }} \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a^{2}}\\---------------\)
5. \(y^{\frac{-5}{2}}.y^{\frac{3}{5}}\\= y^{ \frac{-5}{2} + \frac{3}{5} }= y^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{9} }}=\frac{1}{|y|.\sqrt[10]{ y^{9} }} \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y^{2}|}\\---------------\)
6. \(x^{\frac{5}{6}}.x^{2}\\= x^{ \frac{5}{6} + 2 }= x^{\frac{17}{6}}\\=\sqrt[6]{ x^{17} }=|x^{2}|.\sqrt[6]{ x^{5} }\\---------------\)
7. \(x^{\frac{1}{4}}.x^{\frac{-1}{4}}\\= x^{ \frac{1}{4} + (\frac{-1}{4}) }= x^{0}\\=1\\---------------\)
8. \(a^{\frac{-4}{3}}.a^{\frac{-1}{2}}\\= a^{ \frac{-4}{3} + (\frac{-1}{2}) }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
9. \(a^{\frac{2}{3}}.a^{\frac{-1}{2}}\\= a^{ \frac{2}{3} + (\frac{-1}{2}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
10. \(q^{1}.q^{1}\\= q^{ 1 + 1 }= q^{2}\\\\---------------\)
11. \(q^{\frac{5}{4}}.q^{\frac{3}{2}}\\= q^{ \frac{5}{4} + \frac{3}{2} }= q^{\frac{11}{4}}\\=\sqrt[4]{ q^{11} }=|q^{2}|.\sqrt[4]{ q^{3} }\\---------------\)
12. \(x^{\frac{5}{4}}.x^{\frac{-4}{3}}\\= x^{ \frac{5}{4} + (\frac{-4}{3}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)