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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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