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Werk uit m.b.v. de rekenregels

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

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