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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{6}}\right)^{-1}\\= a^{ \frac{5}{6} . (-1) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
2. \(\left(x^{\frac{1}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{1}{3} . (\frac{-5}{6}) }= x^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ x^{5} }}=\frac{1}{\sqrt[18]{ x^{5} }}. \color{purple}{\frac{\sqrt[18]{ x^{13} }}{\sqrt[18]{ x^{13} }}} \\=\frac{\sqrt[18]{ x^{13} }}{|x|}\\---------------\)
3. \(\left(y^{\frac{3}{5}}\right)^{\frac{-1}{6}}\\= y^{ \frac{3}{5} . (\frac{-1}{6}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
4. \(\left(q^{\frac{1}{6}}\right)^{\frac{2}{5}}\\= q^{ \frac{1}{6} . \frac{2}{5} }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
5. \(\left(y^{\frac{2}{5}}\right)^{-1}\\= y^{ \frac{2}{5} . (-1) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
6. \(\left(y^{\frac{1}{2}}\right)^{1}\\= y^{ \frac{1}{2} . 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
7. \(\left(a^{\frac{-5}{2}}\right)^{-2}\\= a^{ \frac{-5}{2} . (-2) }= a^{5}\\\\---------------\)
8. \(\left(y^{\frac{5}{4}}\right)^{\frac{-5}{2}}\\= y^{ \frac{5}{4} . (\frac{-5}{2}) }= y^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ y^{25} }}\\=\frac{1}{|y^{3}|.\sqrt[8]{ y }}=\frac{1}{|y^{3}|.\sqrt[8]{ y }} \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y^{4}|}\\---------------\)
9. \(\left(q^{1}\right)^{\frac{4}{3}}\\= q^{ 1 . \frac{4}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
10. \(\left(a^{-1}\right)^{\frac{-1}{4}}\\= a^{ -1 . (\frac{-1}{4}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
11. \(\left(y^{-1}\right)^{\frac{2}{3}}\\= y^{ -1 . \frac{2}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
12. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-4}{5} . (\frac{-1}{2}) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)