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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{2}{3}}.y^{\frac{3}{5}}\\= y^{ \frac{2}{3} + \frac{3}{5} }= y^{\frac{19}{15}}\\=\sqrt[15]{ y^{19} }=y.\sqrt[15]{ y^{4} }\\---------------\)
2. \(q^{\frac{-2}{3}}.q^{\frac{5}{6}}\\= q^{ \frac{-2}{3} + \frac{5}{6} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
3. \(a^{-1}.a^{\frac{1}{2}}\\= a^{ -1 + \frac{1}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
4. \(x^{\frac{5}{3}}.x^{\frac{-1}{6}}\\= x^{ \frac{5}{3} + (\frac{-1}{6}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
5. \(x^{\frac{1}{3}}.x^{\frac{-2}{5}}\\= x^{ \frac{1}{3} + (\frac{-2}{5}) }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
6. \(x^{2}.x^{\frac{-5}{4}}\\= x^{ 2 + (\frac{-5}{4}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
7. \(a^{\frac{-1}{6}}.a^{\frac{-3}{2}}\\= a^{ \frac{-1}{6} + (\frac{-3}{2}) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
8. \(x^{\frac{1}{2}}.x^{\frac{4}{3}}\\= x^{ \frac{1}{2} + \frac{4}{3} }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
9. \(x^{\frac{1}{5}}.x^{-2}\\= x^{ \frac{1}{5} + (-2) }= x^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ x^{9} }}\\=\frac{1}{x.\sqrt[5]{ x^{4} }}=\frac{1}{x.\sqrt[5]{ x^{4} }} \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x^{2}}\\---------------\)
10. \(a^{\frac{-3}{4}}.a^{\frac{-1}{6}}\\= a^{ \frac{-3}{4} + (\frac{-1}{6}) }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
11. \(q^{\frac{-3}{4}}.q^{\frac{-1}{5}}\\= q^{ \frac{-3}{4} + (\frac{-1}{5}) }= q^{\frac{-19}{20}}\\=\frac{1}{\sqrt[20]{ q^{19} }}=\frac{1}{\sqrt[20]{ q^{19} }}. \color{purple}{\frac{\sqrt[20]{ q }}{\sqrt[20]{ q }}} \\=\frac{\sqrt[20]{ q }}{|q|}\\---------------\)
12. \(y^{\frac{2}{5}}.y^{\frac{1}{4}}\\= y^{ \frac{2}{5} + \frac{1}{4} }= y^{\frac{13}{20}}\\=\sqrt[20]{ y^{13} }\\---------------\)