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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{4}}\right)^{\frac{1}{6}}\\= q^{ \frac{-1}{4} . \frac{1}{6} }= q^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ q }}=\frac{1}{\sqrt[24]{ q }}. \color{purple}{\frac{\sqrt[24]{ q^{23} }}{\sqrt[24]{ q^{23} }}} \\=\frac{\sqrt[24]{ q^{23} }}{|q|}\\---------------\)
2. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{2} . (\frac{-1}{2}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
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. \(\left(x^{\frac{-1}{4}}\right)^{\frac{2}{5}}\\= x^{ \frac{-1}{4} . \frac{2}{5} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
5. \(\left(q^{\frac{1}{6}}\right)^{\frac{-1}{4}}\\= q^{ \frac{1}{6} . (\frac{-1}{4}) }= q^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ q }}=\frac{1}{\sqrt[24]{ q }}. \color{purple}{\frac{\sqrt[24]{ q^{23} }}{\sqrt[24]{ q^{23} }}} \\=\frac{\sqrt[24]{ q^{23} }}{|q|}\\---------------\)
6. \(\left(q^{\frac{5}{2}}\right)^{-1}\\= q^{ \frac{5}{2} . (-1) }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
7. \(\left(q^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{5} . (\frac{-1}{2}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
8. \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{4} . (\frac{-1}{2}) }= q^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ q }}=\frac{1}{\sqrt[8]{ q }}. \color{purple}{\frac{\sqrt[8]{ q^{7} }}{\sqrt[8]{ q^{7} }}} \\=\frac{\sqrt[8]{ q^{7} }}{|q|}\\---------------\)
9. \(\left(a^{\frac{-5}{4}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-5}{4} . (\frac{-3}{2}) }= a^{\frac{15}{8}}\\=\sqrt[8]{ a^{15} }=|a|.\sqrt[8]{ a^{7} }\\---------------\)
10. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-5}{3}}\\= a^{ \frac{-2}{3} . (\frac{-5}{3}) }= a^{\frac{10}{9}}\\=\sqrt[9]{ a^{10} }=a.\sqrt[9]{ a }\\---------------\)
11. \(\left(a^{2}\right)^{1}\\= a^{ 2 . 1 }= a^{2}\\\\---------------\)
12. \(\left(a^{\frac{5}{2}}\right)^{\frac{3}{2}}\\= a^{ \frac{5}{2} . \frac{3}{2} }= a^{\frac{15}{4}}\\=\sqrt[4]{ a^{15} }=|a^{3}|.\sqrt[4]{ a^{3} }\\---------------\)