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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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