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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(a^{\frac{-1}{2}}.a^{\frac{4}{3}}\\= a^{ \frac{-1}{2} + \frac{4}{3} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
2. \(x^{\frac{-1}{6}}.x^{\frac{-5}{4}}\\= x^{ \frac{-1}{6} + (\frac{-5}{4}) }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
3. \(q^{1}.q^{\frac{2}{3}}\\= q^{ 1 + \frac{2}{3} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
4. \(q^{\frac{3}{2}}.q^{\frac{-1}{3}}\\= q^{ \frac{3}{2} + (\frac{-1}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
5. \(x^{\frac{-1}{5}}.x^{\frac{-4}{3}}\\= x^{ \frac{-1}{5} + (\frac{-4}{3}) }= x^{\frac{-23}{15}}\\=\frac{1}{\sqrt[15]{ x^{23} }}\\=\frac{1}{x.\sqrt[15]{ x^{8} }}=\frac{1}{x.\sqrt[15]{ x^{8} }} \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x^{2}}\\---------------\)
6. \(x^{\frac{3}{5}}.x^{1}\\= x^{ \frac{3}{5} + 1 }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
7. \(x^{1}.x^{\frac{-3}{5}}\\= x^{ 1 + (\frac{-3}{5}) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
8. \(x^{\frac{-1}{4}}.x^{\frac{3}{4}}\\= x^{ \frac{-1}{4} + \frac{3}{4} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
9. \(x^{-1}.x^{\frac{-3}{4}}\\= x^{ -1 + (\frac{-3}{4}) }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
10. \(q^{\frac{-2}{5}}.q^{\frac{-1}{5}}\\= q^{ \frac{-2}{5} + (\frac{-1}{5}) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
11. \(q^{1}.q^{\frac{1}{5}}\\= q^{ 1 + \frac{1}{5} }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
12. \(q^{\frac{3}{2}}.q^{-1}\\= q^{ \frac{3}{2} + (-1) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)