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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{1}{3}}.y^{\frac{5}{4}}\\= y^{ \frac{1}{3} + \frac{5}{4} }= y^{\frac{19}{12}}\\=\sqrt[12]{ y^{19} }=|y|.\sqrt[12]{ y^{7} }\\---------------\)
2. \(q^{\frac{5}{3}}.q^{\frac{5}{2}}\\= q^{ \frac{5}{3} + \frac{5}{2} }= q^{\frac{25}{6}}\\=\sqrt[6]{ q^{25} }=|q^{4}|.\sqrt[6]{ q }\\---------------\)
3. \(x^{\frac{-3}{5}}.x^{\frac{-2}{5}}\\= x^{ \frac{-3}{5} + (\frac{-2}{5}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
4. \(q^{\frac{2}{3}}.q^{\frac{1}{2}}\\= q^{ \frac{2}{3} + \frac{1}{2} }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
5. \(a^{\frac{3}{4}}.a^{-1}\\= a^{ \frac{3}{4} + (-1) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
6. \(q^{1}.q^{\frac{-1}{2}}\\= q^{ 1 + (\frac{-1}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(a^{2}.a^{\frac{-1}{5}}\\= a^{ 2 + (\frac{-1}{5}) }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
8. \(q^{\frac{5}{2}}.q^{\frac{2}{5}}\\= q^{ \frac{5}{2} + \frac{2}{5} }= q^{\frac{29}{10}}\\=\sqrt[10]{ q^{29} }=|q^{2}|.\sqrt[10]{ q^{9} }\\---------------\)
9. \(a^{\frac{-4}{3}}.a^{\frac{4}{3}}\\= a^{ \frac{-4}{3} + \frac{4}{3} }= a^{0}\\=1\\---------------\)
10. \(q^{\frac{-5}{2}}.q^{\frac{-3}{5}}\\= q^{ \frac{-5}{2} + (\frac{-3}{5}) }= q^{\frac{-31}{10}}\\=\frac{1}{\sqrt[10]{ q^{31} }}\\=\frac{1}{|q^{3}|.\sqrt[10]{ q }}=\frac{1}{|q^{3}|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{4}|}\\---------------\)
11. \(x^{1}.x^{1}\\= x^{ 1 + 1 }= x^{2}\\\\---------------\)
12. \(a^{-1}.a^{\frac{5}{4}}\\= a^{ -1 + \frac{5}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)