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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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