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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(a^{\frac{-1}{3}}.a^{\frac{-4}{5}}\\= a^{ \frac{-1}{3} + (\frac{-4}{5}) }= a^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ a^{17} }}\\=\frac{1}{a.\sqrt[15]{ a^{2} }}=\frac{1}{a.\sqrt[15]{ a^{2} }} \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a^{2}}\\---------------\)
2. \(a^{-1}.a^{1}\\= a^{ -1 + 1 }= a^{0}\\=1\\---------------\)
3. \(a^{\frac{1}{4}}.a^{\frac{-1}{5}}\\= a^{ \frac{1}{4} + (\frac{-1}{5}) }= a^{\frac{1}{20}}\\=\sqrt[20]{ a }\\---------------\)
4. \(x^{\frac{3}{5}}.x^{\frac{-4}{5}}\\= x^{ \frac{3}{5} + (\frac{-4}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
5. \(x^{\frac{1}{2}}.x^{\frac{-1}{5}}\\= x^{ \frac{1}{2} + (\frac{-1}{5}) }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
6. \(y^{\frac{1}{3}}.y^{\frac{1}{2}}\\= y^{ \frac{1}{3} + \frac{1}{2} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
7. \(a^{1}.a^{\frac{5}{2}}\\= a^{ 1 + \frac{5}{2} }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
8. \(y^{\frac{-1}{2}}.y^{\frac{3}{5}}\\= y^{ \frac{-1}{2} + \frac{3}{5} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
9. \(y^{\frac{5}{6}}.y^{-1}\\= y^{ \frac{5}{6} + (-1) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
10. \(q^{\frac{1}{2}}.q^{\frac{-1}{2}}\\= q^{ \frac{1}{2} + (\frac{-1}{2}) }= q^{0}\\=1\\---------------\)
11. \(y^{1}.y^{\frac{3}{5}}\\= y^{ 1 + \frac{3}{5} }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
12. \(a^{\frac{-2}{3}}.a^{-1}\\= a^{ \frac{-2}{3} + (-1) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)