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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-1}{5} . (\frac{-1}{2}) }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
2. \(\left(y^{\frac{-1}{4}}\right)^{\frac{3}{2}}\\= y^{ \frac{-1}{4} . \frac{3}{2} }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)
3. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-1}{3} . (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
4. \(\left(y^{-1}\right)^{\frac{-2}{3}}\\= y^{ -1 . (\frac{-2}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
5. \(\left(y^{-2}\right)^{\frac{1}{3}}\\= y^{ -2 . \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
6. \(\left(x^{\frac{3}{5}}\right)^{\frac{-5}{6}}\\= x^{ \frac{3}{5} . (\frac{-5}{6}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{3}{2}}\\= a^{ -1 . \frac{3}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
8. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-4}{3}}\\= x^{ \frac{-1}{2} . (\frac{-4}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
9. \(\left(q^{1}\right)^{\frac{5}{4}}\\= q^{ 1 . \frac{5}{4} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
10. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{5}}\\= x^{ \frac{-1}{2} . \frac{1}{5} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
11. \(\left(x^{\frac{-3}{2}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-3}{2} . (\frac{-1}{3}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\left(q^{\frac{-1}{4}}\right)^{\frac{5}{6}}\\= q^{ \frac{-1}{4} . \frac{5}{6} }= q^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ q^{5} }}=\frac{1}{\sqrt[24]{ q^{5} }}. \color{purple}{\frac{\sqrt[24]{ q^{19} }}{\sqrt[24]{ q^{19} }}} \\=\frac{\sqrt[24]{ q^{19} }}{|q|}\\---------------\)