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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{2} . (\frac{-1}{2}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
2. \(\left(q^{\frac{1}{6}}\right)^{1}\\= q^{ \frac{1}{6} . 1 }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
3. \(\left(q^{\frac{-5}{6}}\right)^{\frac{2}{3}}\\= q^{ \frac{-5}{6} . \frac{2}{3} }= q^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ q^{5} }}=\frac{1}{\sqrt[9]{ q^{5} }}. \color{purple}{\frac{\sqrt[9]{ q^{4} }}{\sqrt[9]{ q^{4} }}} \\=\frac{\sqrt[9]{ q^{4} }}{q}\\---------------\)
4. \(\left(q^{1}\right)^{\frac{4}{5}}\\= q^{ 1 . \frac{4}{5} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
5. \(\left(q^{\frac{3}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{3}{5} . (\frac{-1}{5}) }= q^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ q^{3} }}=\frac{1}{\sqrt[25]{ q^{3} }}. \color{purple}{\frac{\sqrt[25]{ q^{22} }}{\sqrt[25]{ q^{22} }}} \\=\frac{\sqrt[25]{ q^{22} }}{q}\\---------------\)
6. \(\left(q^{\frac{-1}{5}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-1}{5} . (\frac{-5}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
7. \(\left(y^{\frac{2}{3}}\right)^{\frac{1}{4}}\\= y^{ \frac{2}{3} . \frac{1}{4} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
8. \(\left(x^{1}\right)^{\frac{5}{2}}\\= x^{ 1 . \frac{5}{2} }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
9. \(\left(q^{2}\right)^{\frac{1}{2}}\\= q^{ 2 . \frac{1}{2} }= q^{1}\\\\---------------\)
10. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-1}{5}}\\= y^{ \frac{-1}{6} . (\frac{-1}{5}) }= y^{\frac{1}{30}}\\=\sqrt[30]{ y }\\---------------\)
11. \(\left(q^{\frac{1}{6}}\right)^{\frac{-5}{6}}\\= q^{ \frac{1}{6} . (\frac{-5}{6}) }= q^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ q^{5} }}=\frac{1}{\sqrt[36]{ q^{5} }}. \color{purple}{\frac{\sqrt[36]{ q^{31} }}{\sqrt[36]{ q^{31} }}} \\=\frac{\sqrt[36]{ q^{31} }}{|q|}\\---------------\)
12. \(\left(q^{\frac{-5}{2}}\right)^{\frac{5}{2}}\\= q^{ \frac{-5}{2} . \frac{5}{2} }= q^{\frac{-25}{4}}\\=\frac{1}{\sqrt[4]{ q^{25} }}\\=\frac{1}{|q^{6}|.\sqrt[4]{ q }}=\frac{1}{|q^{6}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{7}|}\\---------------\)