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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{4}{3}}.q^{\frac{5}{6}}\\= q^{ \frac{4}{3} + \frac{5}{6} }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
2. \(y^{\frac{4}{3}}.y^{\frac{1}{3}}\\= y^{ \frac{4}{3} + \frac{1}{3} }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
3. \(a^{\frac{3}{5}}.a^{\frac{-1}{4}}\\= a^{ \frac{3}{5} + (\frac{-1}{4}) }= a^{\frac{7}{20}}\\=\sqrt[20]{ a^{7} }\\---------------\)
4. \(x^{\frac{-1}{4}}.x^{\frac{-2}{3}}\\= x^{ \frac{-1}{4} + (\frac{-2}{3}) }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
5. \(a^{\frac{-2}{3}}.a^{\frac{-4}{3}}\\= a^{ \frac{-2}{3} + (\frac{-4}{3}) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
6. \(q^{\frac{5}{3}}.q^{\frac{-3}{5}}\\= q^{ \frac{5}{3} + (\frac{-3}{5}) }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
7. \(x^{\frac{1}{4}}.x^{\frac{5}{3}}\\= x^{ \frac{1}{4} + \frac{5}{3} }= x^{\frac{23}{12}}\\=\sqrt[12]{ x^{23} }=|x|.\sqrt[12]{ x^{11} }\\---------------\)
8. \(a^{\frac{5}{3}}.a^{\frac{1}{6}}\\= a^{ \frac{5}{3} + \frac{1}{6} }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
9. \(q^{\frac{1}{2}}.q^{1}\\= q^{ \frac{1}{2} + 1 }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
10. \(x^{\frac{-1}{4}}.x^{-1}\\= x^{ \frac{-1}{4} + (-1) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
11. \(a^{\frac{1}{5}}.a^{\frac{3}{4}}\\= a^{ \frac{1}{5} + \frac{3}{4} }= a^{\frac{19}{20}}\\=\sqrt[20]{ a^{19} }\\---------------\)
12. \(y^{\frac{-1}{2}}.y^{\frac{-3}{4}}\\= y^{ \frac{-1}{2} + (\frac{-3}{4}) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)