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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{-2}{3} . \frac{1}{2} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-5}{3}}\\= a^{ \frac{-5}{6} . (\frac{-5}{3}) }= a^{\frac{25}{18}}\\=\sqrt[18]{ a^{25} }=|a|.\sqrt[18]{ a^{7} }\\---------------\)
3. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-5}{2}}\\= x^{ \frac{-3}{4} . (\frac{-5}{2}) }= x^{\frac{15}{8}}\\=\sqrt[8]{ x^{15} }=|x|.\sqrt[8]{ x^{7} }\\---------------\)
4. \(\left(x^{\frac{-5}{6}}\right)^{\frac{1}{3}}\\= x^{ \frac{-5}{6} . \frac{1}{3} }= x^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ x^{5} }}=\frac{1}{\sqrt[18]{ x^{5} }}. \color{purple}{\frac{\sqrt[18]{ x^{13} }}{\sqrt[18]{ x^{13} }}} \\=\frac{\sqrt[18]{ x^{13} }}{|x|}\\---------------\)
5. \(\left(x^{\frac{1}{6}}\right)^{\frac{1}{3}}\\= x^{ \frac{1}{6} . \frac{1}{3} }= x^{\frac{1}{18}}\\=\sqrt[18]{ x }\\---------------\)
6. \(\left(q^{1}\right)^{\frac{3}{2}}\\= q^{ 1 . \frac{3}{2} }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
7. \(\left(y^{\frac{1}{2}}\right)^{\frac{5}{4}}\\= y^{ \frac{1}{2} . \frac{5}{4} }= y^{\frac{5}{8}}\\=\sqrt[8]{ y^{5} }\\---------------\)
8. \(\left(a^{\frac{1}{4}}\right)^{\frac{3}{2}}\\= a^{ \frac{1}{4} . \frac{3}{2} }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)
9. \(\left(a^{\frac{4}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{4}{3} . \frac{2}{3} }= a^{\frac{8}{9}}\\=\sqrt[9]{ a^{8} }\\---------------\)
10. \(\left(q^{\frac{1}{6}}\right)^{\frac{-1}{5}}\\= q^{ \frac{1}{6} . (\frac{-1}{5}) }= q^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ q }}=\frac{1}{\sqrt[30]{ q }}. \color{purple}{\frac{\sqrt[30]{ q^{29} }}{\sqrt[30]{ q^{29} }}} \\=\frac{\sqrt[30]{ q^{29} }}{|q|}\\---------------\)
11. \(\left(y^{\frac{5}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{5}{3} . (\frac{-1}{2}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
12. \(\left(x^{\frac{5}{6}}\right)^{\frac{2}{3}}\\= x^{ \frac{5}{6} . \frac{2}{3} }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)