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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{1}.x^{\frac{-5}{6}}\\= x^{ 1 + (\frac{-5}{6}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
2. \(y^{\frac{-1}{2}}.y^{\frac{1}{2}}\\= y^{ \frac{-1}{2} + \frac{1}{2} }= y^{0}\\=1\\---------------\)
3. \(q^{\frac{1}{5}}.q^{-1}\\= q^{ \frac{1}{5} + (-1) }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
4. \(q^{1}.q^{\frac{2}{5}}\\= q^{ 1 + \frac{2}{5} }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
5. \(x^{\frac{2}{3}}.x^{\frac{-5}{6}}\\= x^{ \frac{2}{3} + (\frac{-5}{6}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
6. \(a^{\frac{5}{3}}.a^{\frac{1}{3}}\\= a^{ \frac{5}{3} + \frac{1}{3} }= a^{2}\\\\---------------\)
7. \(x^{\frac{-3}{2}}.x^{\frac{-2}{3}}\\= x^{ \frac{-3}{2} + (\frac{-2}{3}) }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
8. \(a^{1}.a^{\frac{5}{3}}\\= a^{ 1 + \frac{5}{3} }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
9. \(q^{\frac{4}{3}}.q^{\frac{5}{6}}\\= q^{ \frac{4}{3} + \frac{5}{6} }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
10. \(x^{\frac{-3}{4}}.x^{\frac{3}{5}}\\= x^{ \frac{-3}{4} + \frac{3}{5} }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)
11. \(x^{\frac{1}{2}}.x^{\frac{-1}{2}}\\= x^{ \frac{1}{2} + (\frac{-1}{2}) }= x^{0}\\=1\\---------------\)
12. \(y^{-2}.y^{\frac{-5}{4}}\\= y^{ -2 + (\frac{-5}{4}) }= y^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ y^{13} }}\\=\frac{1}{|y^{3}|.\sqrt[4]{ y }}=\frac{1}{|y^{3}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{4}|}\\---------------\)