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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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