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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{3} . (\frac{-1}{2}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
2. \(\left(q^{\frac{2}{3}}\right)^{\frac{-3}{4}}\\= q^{ \frac{2}{3} . (\frac{-3}{4}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-1}{6} . (\frac{-4}{5}) }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
4. \(\left(q^{\frac{5}{2}}\right)^{\frac{-5}{6}}\\= q^{ \frac{5}{2} . (\frac{-5}{6}) }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
5. \(\left(q^{-1}\right)^{\frac{1}{5}}\\= q^{ -1 . \frac{1}{5} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
6. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{2} . \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{-5}{2}}\\= a^{ -1 . (\frac{-5}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
8. \(\left(x^{\frac{3}{5}}\right)^{2}\\= x^{ \frac{3}{5} . 2 }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
9. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-1}{2} . (\frac{-4}{5}) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
10. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-1}{3} . (\frac{-5}{6}) }= y^{\frac{5}{18}}\\=\sqrt[18]{ y^{5} }\\---------------\)
11. \(\left(x^{\frac{-5}{2}}\right)^{\frac{4}{3}}\\= x^{ \frac{-5}{2} . \frac{4}{3} }= x^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ x^{10} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x }}=\frac{1}{x^{3}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{4}}\\---------------\)
12. \(\left(x^{\frac{-5}{4}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-5}{4} . (\frac{-1}{6}) }= x^{\frac{5}{24}}\\=\sqrt[24]{ x^{5} }\\---------------\)