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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(a^{\frac{4}{3}}.a^{\frac{-1}{4}}\\= a^{ \frac{4}{3} + (\frac{-1}{4}) }= a^{\frac{13}{12}}\\=\sqrt[12]{ a^{13} }=|a|.\sqrt[12]{ a }\\---------------\)
2. \(y^{\frac{2}{3}}.y^{-1}\\= y^{ \frac{2}{3} + (-1) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
3. \(a^{\frac{-2}{5}}.a^{\frac{1}{2}}\\= a^{ \frac{-2}{5} + \frac{1}{2} }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
4. \(y^{\frac{2}{5}}.y^{\frac{2}{3}}\\= y^{ \frac{2}{5} + \frac{2}{3} }= y^{\frac{16}{15}}\\=\sqrt[15]{ y^{16} }=y.\sqrt[15]{ y }\\---------------\)
5. \(a^{\frac{-1}{4}}.a^{\frac{1}{4}}\\= a^{ \frac{-1}{4} + \frac{1}{4} }= a^{0}\\=1\\---------------\)
6. \(x^{\frac{-1}{6}}.x^{\frac{1}{2}}\\= x^{ \frac{-1}{6} + \frac{1}{2} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
7. \(x^{\frac{3}{4}}.x^{\frac{-4}{5}}\\= x^{ \frac{3}{4} + (\frac{-4}{5}) }= x^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ x }}=\frac{1}{\sqrt[20]{ x }}. \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x|}\\---------------\)
8. \(a^{\frac{3}{4}}.a^{-1}\\= a^{ \frac{3}{4} + (-1) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
9. \(q^{\frac{3}{2}}.q^{\frac{5}{2}}\\= q^{ \frac{3}{2} + \frac{5}{2} }= q^{4}\\\\---------------\)
10. \(y^{\frac{-1}{2}}.y^{\frac{1}{2}}\\= y^{ \frac{-1}{2} + \frac{1}{2} }= y^{0}\\=1\\---------------\)
11. \(q^{-1}.q^{\frac{-1}{3}}\\= q^{ -1 + (\frac{-1}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
12. \(q^{\frac{3}{4}}.q^{\frac{-5}{2}}\\= q^{ \frac{3}{4} + (\frac{-5}{2}) }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)