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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{-2}{3}}.y^{\frac{-1}{3}}\\= y^{ \frac{-2}{3} + (\frac{-1}{3}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
2. \(x^{\frac{1}{2}}.x^{\frac{1}{6}}\\= x^{ \frac{1}{2} + \frac{1}{6} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
3. \(y^{-1}.y^{1}\\= y^{ -1 + 1 }= y^{0}\\=1\\---------------\)
4. \(a^{\frac{5}{2}}.a^{\frac{-2}{5}}\\= a^{ \frac{5}{2} + (\frac{-2}{5}) }= a^{\frac{21}{10}}\\=\sqrt[10]{ a^{21} }=|a^{2}|.\sqrt[10]{ a }\\---------------\)
5. \(y^{\frac{-1}{3}}.y^{1}\\= y^{ \frac{-1}{3} + 1 }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
6. \(q^{\frac{3}{4}}.q^{\frac{-1}{2}}\\= q^{ \frac{3}{4} + (\frac{-1}{2}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
7. \(y^{\frac{1}{2}}.y^{\frac{1}{3}}\\= y^{ \frac{1}{2} + \frac{1}{3} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
8. \(a^{\frac{1}{2}}.a^{\frac{3}{2}}\\= a^{ \frac{1}{2} + \frac{3}{2} }= a^{2}\\\\---------------\)
9. \(x^{\frac{4}{3}}.x^{\frac{-1}{4}}\\= x^{ \frac{4}{3} + (\frac{-1}{4}) }= x^{\frac{13}{12}}\\=\sqrt[12]{ x^{13} }=|x|.\sqrt[12]{ x }\\---------------\)
10. \(a^{\frac{1}{2}}.a^{\frac{-2}{5}}\\= a^{ \frac{1}{2} + (\frac{-2}{5}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
11. \(x^{\frac{2}{3}}.x^{\frac{4}{3}}\\= x^{ \frac{2}{3} + \frac{4}{3} }= x^{2}\\\\---------------\)
12. \(y^{\frac{1}{6}}.y^{\frac{1}{5}}\\= y^{ \frac{1}{6} + \frac{1}{5} }= y^{\frac{11}{30}}\\=\sqrt[30]{ y^{11} }\\---------------\)