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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{6}}\right)^{\frac{1}{5}}\\= q^{ \frac{-1}{6} . \frac{1}{5} }= q^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ q }}=\frac{1}{\sqrt[30]{ q }}. \color{purple}{\frac{\sqrt[30]{ q^{29} }}{\sqrt[30]{ q^{29} }}} \\=\frac{\sqrt[30]{ q^{29} }}{|q|}\\---------------\)
2. \(\left(q^{\frac{-1}{5}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{5} . (\frac{-2}{5}) }= q^{\frac{2}{25}}\\=\sqrt[25]{ q^{2} }\\---------------\)
3. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-1}{6} . (\frac{-1}{3}) }= q^{\frac{1}{18}}\\=\sqrt[18]{ q }\\---------------\)
4. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-5}{3}}\\= x^{ \frac{-5}{6} . (\frac{-5}{3}) }= x^{\frac{25}{18}}\\=\sqrt[18]{ x^{25} }=|x|.\sqrt[18]{ x^{7} }\\---------------\)
5. \(\left(a^{-1}\right)^{\frac{-1}{3}}\\= a^{ -1 . (\frac{-1}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
6. \(\left(y^{\frac{2}{3}}\right)^{\frac{3}{4}}\\= y^{ \frac{2}{3} . \frac{3}{4} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
7. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\left(x^{1}\right)^{-1}\\= x^{ 1 . (-1) }= x^{-1}\\=\frac{1}{x}\\---------------\)
9. \(\left(a^{\frac{-1}{2}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{2} . \frac{3}{4} }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)
10. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-5}{6} . (\frac{-1}{5}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
11. \(\left(y^{\frac{5}{4}}\right)^{\frac{-5}{2}}\\= y^{ \frac{5}{4} . (\frac{-5}{2}) }= y^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ y^{25} }}\\=\frac{1}{|y^{3}|.\sqrt[8]{ y }}=\frac{1}{|y^{3}|.\sqrt[8]{ y }} \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y^{4}|}\\---------------\)
12. \(\left(x^{\frac{4}{3}}\right)^{\frac{-1}{5}}\\= x^{ \frac{4}{3} . (\frac{-1}{5}) }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)