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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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