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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-1}{4}}.x^{-2}\\= x^{ \frac{-1}{4} + (-2) }= x^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ x^{9} }}\\=\frac{1}{|x^{2}|.\sqrt[4]{ x }}=\frac{1}{|x^{2}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{3}|}\\---------------\)
2. \(a^{\frac{-3}{4}}.a^{\frac{-3}{2}}\\= a^{ \frac{-3}{4} + (\frac{-3}{2}) }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
3. \(y^{\frac{-5}{4}}.y^{\frac{-5}{4}}\\= y^{ \frac{-5}{4} + (\frac{-5}{4}) }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
4. \(q^{\frac{1}{2}}.q^{\frac{3}{4}}\\= q^{ \frac{1}{2} + \frac{3}{4} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
5. \(q^{\frac{2}{3}}.q^{\frac{2}{3}}\\= q^{ \frac{2}{3} + \frac{2}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
6. \(x^{\frac{1}{6}}.x^{\frac{1}{2}}\\= x^{ \frac{1}{6} + \frac{1}{2} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
7. \(q^{-1}.q^{1}\\= q^{ -1 + 1 }= q^{0}\\=1\\---------------\)
8. \(q^{-1}.q^{\frac{-1}{5}}\\= q^{ -1 + (\frac{-1}{5}) }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
9. \(x^{\frac{2}{5}}.x^{\frac{1}{4}}\\= x^{ \frac{2}{5} + \frac{1}{4} }= x^{\frac{13}{20}}\\=\sqrt[20]{ x^{13} }\\---------------\)
10. \(q^{\frac{-3}{5}}.q^{\frac{4}{5}}\\= q^{ \frac{-3}{5} + \frac{4}{5} }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
11. \(x^{\frac{2}{3}}.x^{-2}\\= x^{ \frac{2}{3} + (-2) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
12. \(y^{-1}.y^{\frac{-1}{2}}\\= y^{ -1 + (\frac{-1}{2}) }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)