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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-1}{3}}.x^{\frac{5}{2}}\\= x^{ \frac{-1}{3} + \frac{5}{2} }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
2. \(x^{\frac{5}{2}}.x^{\frac{-1}{3}}\\= x^{ \frac{5}{2} + (\frac{-1}{3}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
3. \(a^{2}.a^{\frac{1}{2}}\\= a^{ 2 + \frac{1}{2} }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
4. \(a^{\frac{5}{3}}.a^{\frac{-1}{2}}\\= a^{ \frac{5}{3} + (\frac{-1}{2}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
5. \(q^{-1}.q^{\frac{4}{3}}\\= q^{ -1 + \frac{4}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
6. \(x^{\frac{5}{6}}.x^{\frac{-1}{6}}\\= x^{ \frac{5}{6} + (\frac{-1}{6}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
7. \(y^{\frac{-2}{3}}.y^{\frac{1}{5}}\\= y^{ \frac{-2}{3} + \frac{1}{5} }= y^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ y^{7} }}=\frac{1}{\sqrt[15]{ y^{7} }}. \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y}\\---------------\)
8. \(q^{\frac{3}{4}}.q^{\frac{1}{3}}\\= q^{ \frac{3}{4} + \frac{1}{3} }= q^{\frac{13}{12}}\\=\sqrt[12]{ q^{13} }=|q|.\sqrt[12]{ q }\\---------------\)
9. \(a^{-1}.a^{\frac{-1}{3}}\\= a^{ -1 + (\frac{-1}{3}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
10. \(y^{-1}.y^{1}\\= y^{ -1 + 1 }= y^{0}\\=1\\---------------\)
11. \(q^{\frac{-3}{2}}.q^{\frac{5}{3}}\\= q^{ \frac{-3}{2} + \frac{5}{3} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
12. \(y^{2}.y^{\frac{5}{6}}\\= y^{ 2 + \frac{5}{6} }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)