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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{4}}\right)^{\frac{-3}{4}}\\= x^{ \frac{1}{4} . (\frac{-3}{4}) }= x^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ x^{3} }}=\frac{1}{\sqrt[16]{ x^{3} }}. \color{purple}{\frac{\sqrt[16]{ x^{13} }}{\sqrt[16]{ x^{13} }}} \\=\frac{\sqrt[16]{ x^{13} }}{|x|}\\---------------\)
2. \(\left(q^{\frac{2}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{2}{5} . \frac{2}{3} }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
3. \(\left(q^{\frac{-3}{4}}\right)^{\frac{1}{5}}\\= q^{ \frac{-3}{4} . \frac{1}{5} }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
4. \(\left(a^{1}\right)^{\frac{3}{2}}\\= a^{ 1 . \frac{3}{2} }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
5. \(\left(x^{\frac{1}{5}}\right)^{\frac{3}{5}}\\= x^{ \frac{1}{5} . \frac{3}{5} }= x^{\frac{3}{25}}\\=\sqrt[25]{ x^{3} }\\---------------\)
6. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-5}{6} . (\frac{-4}{5}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
7. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-4}{3} . (\frac{-1}{3}) }= q^{\frac{4}{9}}\\=\sqrt[9]{ q^{4} }\\---------------\)
8. \(\left(q^{\frac{2}{3}}\right)^{\frac{5}{3}}\\= q^{ \frac{2}{3} . \frac{5}{3} }= q^{\frac{10}{9}}\\=\sqrt[9]{ q^{10} }=q.\sqrt[9]{ q }\\---------------\)
9. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-5}{6} . (\frac{-1}{2}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
10. \(\left(q^{\frac{4}{5}}\right)^{\frac{1}{4}}\\= q^{ \frac{4}{5} . \frac{1}{4} }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
11. \(\left(x^{\frac{5}{4}}\right)^{\frac{1}{3}}\\= x^{ \frac{5}{4} . \frac{1}{3} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
12. \(\left(x^{\frac{1}{2}}\right)^{\frac{5}{4}}\\= x^{ \frac{1}{2} . \frac{5}{4} }= x^{\frac{5}{8}}\\=\sqrt[8]{ x^{5} }\\---------------\)