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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(a^{\frac{3}{5}}.a^{\frac{4}{5}}\\= a^{ \frac{3}{5} + \frac{4}{5} }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
2. \(a^{1}.a^{\frac{2}{5}}\\= a^{ 1 + \frac{2}{5} }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
3. \(q^{\frac{-1}{3}}.q^{\frac{1}{2}}\\= q^{ \frac{-1}{3} + \frac{1}{2} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
4. \(a^{\frac{1}{2}}.a^{1}\\= a^{ \frac{1}{2} + 1 }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
5. \(x^{\frac{1}{3}}.x^{\frac{1}{3}}\\= x^{ \frac{1}{3} + \frac{1}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
6. \(a^{\frac{3}{5}}.a^{\frac{-1}{6}}\\= a^{ \frac{3}{5} + (\frac{-1}{6}) }= a^{\frac{13}{30}}\\=\sqrt[30]{ a^{13} }\\---------------\)
7. \(a^{\frac{1}{3}}.a^{-1}\\= a^{ \frac{1}{3} + (-1) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
8. \(q^{\frac{2}{3}}.q^{1}\\= q^{ \frac{2}{3} + 1 }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
9. \(q^{\frac{4}{5}}.q^{\frac{3}{4}}\\= q^{ \frac{4}{5} + \frac{3}{4} }= q^{\frac{31}{20}}\\=\sqrt[20]{ q^{31} }=|q|.\sqrt[20]{ q^{11} }\\---------------\)
10. \(x^{\frac{-5}{4}}.x^{\frac{4}{5}}\\= x^{ \frac{-5}{4} + \frac{4}{5} }= x^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ x^{9} }}=\frac{1}{\sqrt[20]{ x^{9} }}. \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x|}\\---------------\)
11. \(a^{\frac{-1}{3}}.a^{\frac{4}{5}}\\= a^{ \frac{-1}{3} + \frac{4}{5} }= a^{\frac{7}{15}}\\=\sqrt[15]{ a^{7} }\\---------------\)
12. \(y^{\frac{3}{5}}.y^{\frac{-1}{2}}\\= y^{ \frac{3}{5} + (\frac{-1}{2}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)