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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-2}{3} . (\frac{-1}{2}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
2. \(\left(x^{\frac{-5}{6}}\right)^{\frac{5}{2}}\\= x^{ \frac{-5}{6} . \frac{5}{2} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
3. \(\left(y^{\frac{1}{6}}\right)^{\frac{-1}{6}}\\= y^{ \frac{1}{6} . (\frac{-1}{6}) }= y^{\frac{-1}{36}}\\=\frac{1}{\sqrt[36]{ y }}=\frac{1}{\sqrt[36]{ y }}. \color{purple}{\frac{\sqrt[36]{ y^{35} }}{\sqrt[36]{ y^{35} }}} \\=\frac{\sqrt[36]{ y^{35} }}{|y|}\\---------------\)
4. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-3}{5} . (\frac{-2}{3}) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
5. \(\left(x^{\frac{-1}{2}}\right)^{\frac{5}{6}}\\= x^{ \frac{-1}{2} . \frac{5}{6} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
6. \(\left(y^{\frac{-4}{3}}\right)^{\frac{-5}{2}}\\= y^{ \frac{-4}{3} . (\frac{-5}{2}) }= y^{\frac{10}{3}}\\=\sqrt[3]{ y^{10} }=y^{3}.\sqrt[3]{ y }\\---------------\)
7. \(\left(q^{\frac{5}{6}}\right)^{1}\\= q^{ \frac{5}{6} . 1 }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
8. \(\left(q^{\frac{-5}{4}}\right)^{\frac{1}{3}}\\= q^{ \frac{-5}{4} . \frac{1}{3} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
9. \(\left(a^{\frac{1}{2}}\right)^{\frac{3}{4}}\\= a^{ \frac{1}{2} . \frac{3}{4} }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)
10. \(\left(q^{\frac{-4}{5}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-4}{5} . (\frac{-4}{5}) }= q^{\frac{16}{25}}\\=\sqrt[25]{ q^{16} }\\---------------\)
11. \(\left(q^{-1}\right)^{-1}\\= q^{ -1 . (-1) }= q^{1}\\\\---------------\)
12. \(\left(y^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= y^{ \frac{1}{2} . (\frac{-3}{4}) }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)