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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{1}.y^{1}\\= y^{ 1 + 1 }= y^{2}\\\\---------------\)
2. \(x^{\frac{-4}{3}}.x^{-1}\\= x^{ \frac{-4}{3} + (-1) }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
3. \(y^{\frac{-1}{2}}.y^{2}\\= y^{ \frac{-1}{2} + 2 }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
4. \(q^{\frac{1}{2}}.q^{\frac{-1}{3}}\\= q^{ \frac{1}{2} + (\frac{-1}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
5. \(x^{\frac{3}{4}}.x^{\frac{2}{5}}\\= x^{ \frac{3}{4} + \frac{2}{5} }= x^{\frac{23}{20}}\\=\sqrt[20]{ x^{23} }=|x|.\sqrt[20]{ x^{3} }\\---------------\)
6. \(q^{\frac{1}{2}}.q^{\frac{-5}{6}}\\= q^{ \frac{1}{2} + (\frac{-5}{6}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(y^{\frac{1}{3}}.y^{\frac{5}{6}}\\= y^{ \frac{1}{3} + \frac{5}{6} }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
8. \(x^{\frac{2}{3}}.x^{\frac{1}{4}}\\= x^{ \frac{2}{3} + \frac{1}{4} }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)
9. \(q^{\frac{1}{3}}.q^{\frac{1}{6}}\\= q^{ \frac{1}{3} + \frac{1}{6} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(y^{\frac{1}{5}}.y^{\frac{-1}{3}}\\= y^{ \frac{1}{5} + (\frac{-1}{3}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
11. \(q^{\frac{2}{3}}.q^{\frac{-2}{3}}\\= q^{ \frac{2}{3} + (\frac{-2}{3}) }= q^{0}\\=1\\---------------\)
12. \(y^{\frac{4}{5}}.y^{-1}\\= y^{ \frac{4}{5} + (-1) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)