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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{-1}\right)^{\frac{-1}{3}}\\= y^{ -1 . (\frac{-1}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
2. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-1}{2} . (\frac{-3}{5}) }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
3. \(\left(a^{\frac{-1}{6}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-1}{6} . (\frac{-1}{6}) }= a^{\frac{1}{36}}\\=\sqrt[36]{ a }\\---------------\)
4. \(\left(a^{\frac{3}{2}}\right)^{1}\\= a^{ \frac{3}{2} . 1 }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
5. \(\left(x^{\frac{1}{3}}\right)^{-1}\\= x^{ \frac{1}{3} . (-1) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\left(x^{\frac{-5}{6}}\right)^{\frac{4}{5}}\\= x^{ \frac{-5}{6} . \frac{4}{5} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
7. \(\left(a^{1}\right)^{\frac{1}{3}}\\= a^{ 1 . \frac{1}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
8. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{2} . (\frac{-1}{2}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
9. \(\left(q^{\frac{3}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{3}{2} . (\frac{-2}{3}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
10. \(\left(x^{\frac{1}{2}}\right)^{\frac{4}{3}}\\= x^{ \frac{1}{2} . \frac{4}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
11. \(\left(x^{\frac{-3}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-3}{2} . \frac{1}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
12. \(\left(q^{-1}\right)^{\frac{-1}{5}}\\= q^{ -1 . (\frac{-1}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)