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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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