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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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