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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{4}}\right)^{2}\\= x^{ \frac{-1}{4} . 2 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
2. \(\left(x^{1}\right)^{\frac{2}{3}}\\= x^{ 1 . \frac{2}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
3. \(\left(q^{\frac{3}{2}}\right)^{\frac{1}{5}}\\= q^{ \frac{3}{2} . \frac{1}{5} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
4. \(\left(x^{\frac{1}{2}}\right)^{\frac{2}{5}}\\= x^{ \frac{1}{2} . \frac{2}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
5. \(\left(x^{\frac{-5}{4}}\right)^{\frac{5}{3}}\\= x^{ \frac{-5}{4} . \frac{5}{3} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
6. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-5}{4} . (\frac{-2}{5}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(\left(y^{\frac{1}{4}}\right)^{\frac{4}{3}}\\= y^{ \frac{1}{4} . \frac{4}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
8. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-1}{2} . (\frac{-1}{5}) }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
9. \(\left(x^{\frac{-3}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{-3}{4} . \frac{1}{2} }= x^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ x^{3} }}=\frac{1}{\sqrt[8]{ x^{3} }}. \color{purple}{\frac{\sqrt[8]{ x^{5} }}{\sqrt[8]{ x^{5} }}} \\=\frac{\sqrt[8]{ x^{5} }}{|x|}\\---------------\)
10. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-5}{6}}\\= q^{ \frac{-1}{2} . (\frac{-5}{6}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
11. \(\left(a^{-1}\right)^{\frac{-1}{2}}\\= a^{ -1 . (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\left(x^{\frac{-1}{6}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-1}{6} . (\frac{-5}{4}) }= x^{\frac{5}{24}}\\=\sqrt[24]{ x^{5} }\\---------------\)