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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{2}.q^{\frac{2}{5}}\\= q^{ 2 + \frac{2}{5} }= q^{\frac{12}{5}}\\=\sqrt[5]{ q^{12} }=q^{2}.\sqrt[5]{ q^{2} }\\---------------\)
2. \(y^{\frac{1}{2}}.y^{\frac{5}{2}}\\= y^{ \frac{1}{2} + \frac{5}{2} }= y^{3}\\\\---------------\)
3. \(q^{\frac{-5}{4}}.q^{\frac{1}{4}}\\= q^{ \frac{-5}{4} + \frac{1}{4} }= q^{-1}\\=\frac{1}{q}\\---------------\)
4. \(x^{1}.x^{\frac{1}{5}}\\= x^{ 1 + \frac{1}{5} }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
5. \(x^{\frac{-2}{3}}.x^{\frac{1}{5}}\\= x^{ \frac{-2}{3} + \frac{1}{5} }= x^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ x^{7} }}=\frac{1}{\sqrt[15]{ x^{7} }}. \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x}\\---------------\)
6. \(q^{\frac{-1}{2}}.q^{-1}\\= q^{ \frac{-1}{2} + (-1) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
7. \(x^{\frac{1}{6}}.x^{\frac{-1}{5}}\\= x^{ \frac{1}{6} + (\frac{-1}{5}) }= x^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ x }}=\frac{1}{\sqrt[30]{ x }}. \color{purple}{\frac{\sqrt[30]{ x^{29} }}{\sqrt[30]{ x^{29} }}} \\=\frac{\sqrt[30]{ x^{29} }}{|x|}\\---------------\)
8. \(x^{\frac{3}{4}}.x^{\frac{-1}{3}}\\= x^{ \frac{3}{4} + (\frac{-1}{3}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
9. \(a^{\frac{-5}{6}}.a^{\frac{-2}{3}}\\= a^{ \frac{-5}{6} + (\frac{-2}{3}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
10. \(x^{\frac{-5}{3}}.x^{-1}\\= x^{ \frac{-5}{3} + (-1) }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
11. \(x^{\frac{-1}{2}}.x^{2}\\= x^{ \frac{-1}{2} + 2 }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
12. \(q^{\frac{1}{2}}.q^{\frac{-5}{2}}\\= q^{ \frac{1}{2} + (\frac{-5}{2}) }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)