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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{4}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-1}{4} . (\frac{-4}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
2. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{3}}\\= a^{ \frac{5}{6} . \frac{1}{3} }= a^{\frac{5}{18}}\\=\sqrt[18]{ a^{5} }\\---------------\)
3. \(\left(a^{-1}\right)^{\frac{-1}{2}}\\= a^{ -1 . (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
4. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-2}{3} . (\frac{-2}{5}) }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
5. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-5}{6}}\\= a^{ \frac{-2}{3} . (\frac{-5}{6}) }= a^{\frac{5}{9}}\\=\sqrt[9]{ a^{5} }\\---------------\)
6. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{6}}\\= y^{ \frac{1}{2} . (\frac{-1}{6}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
7. \(\left(x^{\frac{5}{6}}\right)^{\frac{5}{6}}\\= x^{ \frac{5}{6} . \frac{5}{6} }= x^{\frac{25}{36}}\\=\sqrt[36]{ x^{25} }\\---------------\)
8. \(\left(q^{-1}\right)^{\frac{-4}{5}}\\= q^{ -1 . (\frac{-4}{5}) }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
9. \(\left(a^{\frac{-3}{5}}\right)^{1}\\= a^{ \frac{-3}{5} . 1 }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
10. \(\left(q^{\frac{-5}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-5}{3} . \frac{1}{2} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
11. \(\left(x^{-1}\right)^{\frac{2}{3}}\\= x^{ -1 . \frac{2}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-1}{2} . (\frac{-3}{4}) }= q^{\frac{3}{8}}\\=\sqrt[8]{ q^{3} }\\---------------\)