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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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