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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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