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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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