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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{4}{3}}.y^{\frac{3}{4}}\\= y^{ \frac{4}{3} + \frac{3}{4} }= y^{\frac{25}{12}}\\=\sqrt[12]{ y^{25} }=|y^{2}|.\sqrt[12]{ y }\\---------------\)
2. \(y^{\frac{-1}{6}}.y^{\frac{1}{4}}\\= y^{ \frac{-1}{6} + \frac{1}{4} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
3. \(q^{1}.q^{\frac{-1}{3}}\\= q^{ 1 + (\frac{-1}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
4. \(q^{\frac{-1}{3}}.q^{\frac{1}{3}}\\= q^{ \frac{-1}{3} + \frac{1}{3} }= q^{0}\\=1\\---------------\)
5. \(a^{2}.a^{\frac{-5}{4}}\\= a^{ 2 + (\frac{-5}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
6. \(a^{\frac{-3}{5}}.a^{\frac{-4}{3}}\\= a^{ \frac{-3}{5} + (\frac{-4}{3}) }= a^{\frac{-29}{15}}\\=\frac{1}{\sqrt[15]{ a^{29} }}\\=\frac{1}{a.\sqrt[15]{ a^{14} }}=\frac{1}{a.\sqrt[15]{ a^{14} }} \color{purple}{\frac{\sqrt[15]{ a }}{\sqrt[15]{ a }}} \\=\frac{\sqrt[15]{ a }}{a^{2}}\\---------------\)
7. \(x^{1}.x^{\frac{-1}{4}}\\= x^{ 1 + (\frac{-1}{4}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
8. \(y^{\frac{1}{2}}.y^{\frac{-2}{3}}\\= y^{ \frac{1}{2} + (\frac{-2}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
9. \(a^{-1}.a^{\frac{3}{4}}\\= a^{ -1 + \frac{3}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
10. \(y^{\frac{5}{3}}.y^{1}\\= y^{ \frac{5}{3} + 1 }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
11. \(y^{\frac{5}{3}}.y^{\frac{-4}{5}}\\= y^{ \frac{5}{3} + (\frac{-4}{5}) }= y^{\frac{13}{15}}\\=\sqrt[15]{ y^{13} }\\---------------\)
12. \(x^{\frac{5}{6}}.x^{\frac{-5}{4}}\\= x^{ \frac{5}{6} + (\frac{-5}{4}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)