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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{4} . (\frac{-1}{3}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
2. \(\left(x^{-1}\right)^{\frac{-1}{2}}\\= x^{ -1 . (\frac{-1}{2}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
3. \(\left(x^{\frac{1}{3}}\right)^{-2}\\= x^{ \frac{1}{3} . (-2) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
4. \(\left(a^{\frac{5}{6}}\right)^{\frac{-1}{6}}\\= a^{ \frac{5}{6} . (\frac{-1}{6}) }= a^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ a^{5} }}=\frac{1}{\sqrt[36]{ a^{5} }}. \color{purple}{\frac{\sqrt[36]{ a^{31} }}{\sqrt[36]{ a^{31} }}} \\=\frac{\sqrt[36]{ a^{31} }}{|a|}\\---------------\)
5. \(\left(y^{-2}\right)^{1}\\= y^{ -2 . 1 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
6. \(\left(a^{\frac{1}{4}}\right)^{\frac{-2}{5}}\\= a^{ \frac{1}{4} . (\frac{-2}{5}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
7. \(\left(a^{\frac{-5}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-5}{2} . (\frac{-1}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
8. \(\left(q^{1}\right)^{\frac{-3}{2}}\\= q^{ 1 . (\frac{-3}{2}) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
9. \(\left(q^{\frac{5}{2}}\right)^{\frac{1}{6}}\\= q^{ \frac{5}{2} . \frac{1}{6} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
10. \(\left(x^{-2}\right)^{\frac{-5}{4}}\\= x^{ -2 . (\frac{-5}{4}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
11. \(\left(x^{\frac{-2}{3}}\right)^{\frac{4}{3}}\\= x^{ \frac{-2}{3} . \frac{4}{3} }= x^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ x^{8} }}=\frac{1}{\sqrt[9]{ x^{8} }}. \color{purple}{\frac{\sqrt[9]{ x }}{\sqrt[9]{ x }}} \\=\frac{\sqrt[9]{ x }}{x}\\---------------\)
12. \(\left(a^{1}\right)^{\frac{-5}{2}}\\= a^{ 1 . (\frac{-5}{2}) }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)