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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{5}{2}}.q^{\frac{-2}{5}}\\= q^{ \frac{5}{2} + (\frac{-2}{5}) }= q^{\frac{21}{10}}\\=\sqrt[10]{ q^{21} }=|q^{2}|.\sqrt[10]{ q }\\---------------\)
2. \(q^{\frac{1}{6}}.q^{\frac{5}{3}}\\= q^{ \frac{1}{6} + \frac{5}{3} }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
3. \(y^{\frac{-3}{2}}.y^{1}\\= y^{ \frac{-3}{2} + 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
4. \(q^{\frac{5}{6}}.q^{\frac{-2}{3}}\\= q^{ \frac{5}{6} + (\frac{-2}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
5. \(x^{\frac{1}{4}}.x^{\frac{1}{6}}\\= x^{ \frac{1}{4} + \frac{1}{6} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
6. \(a^{\frac{2}{3}}.a^{\frac{3}{5}}\\= a^{ \frac{2}{3} + \frac{3}{5} }= a^{\frac{19}{15}}\\=\sqrt[15]{ a^{19} }=a.\sqrt[15]{ a^{4} }\\---------------\)
7. \(q^{\frac{-2}{3}}.q^{\frac{5}{4}}\\= q^{ \frac{-2}{3} + \frac{5}{4} }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
8. \(a^{-1}.a^{1}\\= a^{ -1 + 1 }= a^{0}\\=1\\---------------\)
9. \(y^{\frac{1}{5}}.y^{\frac{5}{6}}\\= y^{ \frac{1}{5} + \frac{5}{6} }= y^{\frac{31}{30}}\\=\sqrt[30]{ y^{31} }=|y|.\sqrt[30]{ y }\\---------------\)
10. \(x^{1}.x^{\frac{-5}{3}}\\= x^{ 1 + (\frac{-5}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
11. \(x^{\frac{-5}{2}}.x^{\frac{1}{3}}\\= x^{ \frac{-5}{2} + \frac{1}{3} }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
12. \(q^{\frac{-2}{3}}.q^{\frac{1}{3}}\\= q^{ \frac{-2}{3} + \frac{1}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)