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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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