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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{\frac{5}{4}}\\= q^{ -1 . \frac{5}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
2. \(\left(a^{1}\right)^{\frac{-1}{6}}\\= a^{ 1 . (\frac{-1}{6}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{3}{5}}\\= a^{ \frac{-1}{3} . \frac{3}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
4. \(\left(a^{\frac{2}{5}}\right)^{\frac{-1}{3}}\\= a^{ \frac{2}{5} . (\frac{-1}{3}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
5. \(\left(q^{\frac{-5}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-5}{3} . \frac{1}{2} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
6. \(\left(q^{\frac{1}{6}}\right)^{\frac{1}{3}}\\= q^{ \frac{1}{6} . \frac{1}{3} }= q^{\frac{1}{18}}\\=\sqrt[18]{ q }\\---------------\)
7. \(\left(q^{\frac{-2}{5}}\right)^{\frac{3}{4}}\\= q^{ \frac{-2}{5} . \frac{3}{4} }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
8. \(\left(x^{1}\right)^{-1}\\= x^{ 1 . (-1) }= x^{-1}\\=\frac{1}{x}\\---------------\)
9. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-2}{3} . (\frac{-2}{3}) }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)
10. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{2} . \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
11. \(\left(x^{\frac{1}{4}}\right)^{\frac{4}{5}}\\= x^{ \frac{1}{4} . \frac{4}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
12. \(\left(q^{2}\right)^{-2}\\= q^{ 2 . (-2) }= q^{-4}\\=\frac{1}{q^{4}}\\---------------\)