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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{6}}\right)^{\frac{5}{3}}\\= q^{ \frac{-5}{6} . \frac{5}{3} }= q^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ q^{25} }}\\=\frac{1}{|q|.\sqrt[18]{ q^{7} }}=\frac{1}{|q|.\sqrt[18]{ q^{7} }} \color{purple}{\frac{\sqrt[18]{ q^{11} }}{\sqrt[18]{ q^{11} }}} \\=\frac{\sqrt[18]{ q^{11} }}{|q^{2}|}\\---------------\)
2. \(\left(a^{\frac{-1}{3}}\right)^{-2}\\= a^{ \frac{-1}{3} . (-2) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
3. \(\left(x^{\frac{-5}{2}}\right)^{\frac{1}{6}}\\= x^{ \frac{-5}{2} . \frac{1}{6} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
4. \(\left(q^{\frac{5}{6}}\right)^{1}\\= q^{ \frac{5}{6} . 1 }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
5. \(\left(a^{\frac{5}{2}}\right)^{1}\\= a^{ \frac{5}{2} . 1 }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
6. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-2}{5}}\\= x^{ \frac{-1}{2} . (\frac{-2}{5}) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
7. \(\left(x^{\frac{1}{3}}\right)^{\frac{1}{6}}\\= x^{ \frac{1}{3} . \frac{1}{6} }= x^{\frac{1}{18}}\\=\sqrt[18]{ x }\\---------------\)
8. \(\left(a^{\frac{3}{5}}\right)^{\frac{-2}{5}}\\= a^{ \frac{3}{5} . (\frac{-2}{5}) }= a^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ a^{6} }}=\frac{1}{\sqrt[25]{ a^{6} }}. \color{purple}{\frac{\sqrt[25]{ a^{19} }}{\sqrt[25]{ a^{19} }}} \\=\frac{\sqrt[25]{ a^{19} }}{a}\\---------------\)
9. \(\left(a^{\frac{5}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{5}{3} . (\frac{-2}{3}) }= a^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ a^{10} }}\\=\frac{1}{a.\sqrt[9]{ a }}=\frac{1}{a.\sqrt[9]{ a }} \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a^{2}}\\---------------\)
10. \(\left(x^{\frac{1}{6}}\right)^{-1}\\= x^{ \frac{1}{6} . (-1) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
11. \(\left(q^{\frac{1}{5}}\right)^{\frac{-2}{3}}\\= q^{ \frac{1}{5} . (\frac{-2}{3}) }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
12. \(\left(x^{2}\right)^{\frac{-3}{5}}\\= x^{ 2 . (\frac{-3}{5}) }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)