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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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