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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{4}}\right)^{\frac{5}{4}}\\= y^{ \frac{-1}{4} . \frac{5}{4} }= y^{\frac{-5}{16}}\\=\frac{1}{\sqrt[16]{ y^{5} }}=\frac{1}{\sqrt[16]{ y^{5} }}. \color{purple}{\frac{\sqrt[16]{ y^{11} }}{\sqrt[16]{ y^{11} }}} \\=\frac{\sqrt[16]{ y^{11} }}{|y|}\\---------------\)
2. \(\left(y^{\frac{2}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{2}{5} . \frac{1}{3} }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
3. \(\left(x^{\frac{1}{4}}\right)^{-1}\\= x^{ \frac{1}{4} . (-1) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
4. \(\left(y^{\frac{5}{4}}\right)^{\frac{1}{3}}\\= y^{ \frac{5}{4} . \frac{1}{3} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
5. \(\left(y^{-1}\right)^{-1}\\= y^{ -1 . (-1) }= y^{1}\\\\---------------\)
6. \(\left(q^{\frac{2}{5}}\right)^{1}\\= q^{ \frac{2}{5} . 1 }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
7. \(\left(q^{\frac{5}{3}}\right)^{\frac{-5}{4}}\\= q^{ \frac{5}{3} . (\frac{-5}{4}) }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
8. \(\left(y^{\frac{1}{6}}\right)^{1}\\= y^{ \frac{1}{6} . 1 }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
9. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{6}}\\= y^{ \frac{1}{2} . \frac{1}{6} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
10. \(\left(y^{\frac{-1}{4}}\right)^{\frac{3}{5}}\\= y^{ \frac{-1}{4} . \frac{3}{5} }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
11. \(\left(y^{1}\right)^{\frac{1}{6}}\\= y^{ 1 . \frac{1}{6} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{\frac{5}{6}}\\= q^{ \frac{-1}{2} . \frac{5}{6} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)