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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{3}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-5}{3} . (\frac{-3}{2}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
2. \(\left(y^{\frac{5}{6}}\right)^{\frac{5}{6}}\\= y^{ \frac{5}{6} . \frac{5}{6} }= y^{\frac{25}{36}}\\=\sqrt[36]{ y^{25} }\\---------------\)
3. \(\left(x^{\frac{5}{6}}\right)^{\frac{-1}{2}}\\= x^{ \frac{5}{6} . (\frac{-1}{2}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
4. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-5}{3} . (\frac{-1}{3}) }= y^{\frac{5}{9}}\\=\sqrt[9]{ y^{5} }\\---------------\)
5. \(\left(a^{\frac{1}{5}}\right)^{1}\\= a^{ \frac{1}{5} . 1 }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
6. \(\left(a^{\frac{3}{5}}\right)^{1}\\= a^{ \frac{3}{5} . 1 }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
7. \(\left(q^{\frac{5}{4}}\right)^{\frac{-1}{6}}\\= q^{ \frac{5}{4} . (\frac{-1}{6}) }= q^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ q^{5} }}=\frac{1}{\sqrt[24]{ q^{5} }}. \color{purple}{\frac{\sqrt[24]{ q^{19} }}{\sqrt[24]{ q^{19} }}} \\=\frac{\sqrt[24]{ q^{19} }}{|q|}\\---------------\)
8. \(\left(y^{\frac{2}{5}}\right)^{-2}\\= y^{ \frac{2}{5} . (-2) }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
9. \(\left(x^{-1}\right)^{\frac{1}{5}}\\= x^{ -1 . \frac{1}{5} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
10. \(\left(y^{\frac{5}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{5}{2} . \frac{1}{2} }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
11. \(\left(x^{\frac{3}{4}}\right)^{\frac{1}{6}}\\= x^{ \frac{3}{4} . \frac{1}{6} }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
12. \(\left(x^{\frac{2}{3}}\right)^{\frac{5}{6}}\\= x^{ \frac{2}{3} . \frac{5}{6} }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)