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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-2}\right)^{\frac{1}{6}}\\= q^{ -2 . \frac{1}{6} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
2. \(\left(y^{\frac{3}{5}}\right)^{\frac{-3}{4}}\\= y^{ \frac{3}{5} . (\frac{-3}{4}) }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
3. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-1}{6}}\\= y^{ \frac{-5}{6} . (\frac{-1}{6}) }= y^{\frac{5}{36}}\\=\sqrt[36]{ y^{5} }\\---------------\)
4. \(\left(y^{\frac{5}{2}}\right)^{\frac{-5}{2}}\\= y^{ \frac{5}{2} . (\frac{-5}{2}) }= y^{\frac{-25}{4}}\\=\frac{1}{\sqrt[4]{ y^{25} }}\\=\frac{1}{|y^{6}|.\sqrt[4]{ y }}=\frac{1}{|y^{6}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{7}|}\\---------------\)
5. \(\left(a^{\frac{-5}{6}}\right)^{\frac{1}{3}}\\= a^{ \frac{-5}{6} . \frac{1}{3} }= a^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ a^{5} }}=\frac{1}{\sqrt[18]{ a^{5} }}. \color{purple}{\frac{\sqrt[18]{ a^{13} }}{\sqrt[18]{ a^{13} }}} \\=\frac{\sqrt[18]{ a^{13} }}{|a|}\\---------------\)
6. \(\left(x^{\frac{5}{6}}\right)^{\frac{1}{3}}\\= x^{ \frac{5}{6} . \frac{1}{3} }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)
7. \(\left(x^{1}\right)^{\frac{-1}{2}}\\= x^{ 1 . (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\left(q^{\frac{4}{5}}\right)^{1}\\= q^{ \frac{4}{5} . 1 }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
9. \(\left(q^{\frac{2}{3}}\right)^{2}\\= q^{ \frac{2}{3} . 2 }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
10. \(\left(a^{\frac{5}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{5}{3} . \frac{1}{3} }= a^{\frac{5}{9}}\\=\sqrt[9]{ a^{5} }\\---------------\)
11. \(\left(q^{\frac{5}{3}}\right)^{\frac{-4}{3}}\\= q^{ \frac{5}{3} . (\frac{-4}{3}) }= q^{\frac{-20}{9}}\\=\frac{1}{\sqrt[9]{ q^{20} }}\\=\frac{1}{q^{2}.\sqrt[9]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[9]{ q^{2} }} \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q^{3}}\\---------------\)
12. \(\left(a^{\frac{-2}{3}}\right)^{-1}\\= a^{ \frac{-2}{3} . (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)