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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{6}}\\= y^{ \frac{1}{2} . \frac{1}{6} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
2. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)
3. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-1}{2} . (\frac{-4}{5}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
4. \(\left(x^{\frac{2}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{2}{3} . (\frac{-2}{3}) }= x^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ x^{4} }}=\frac{1}{\sqrt[9]{ x^{4} }}. \color{purple}{\frac{\sqrt[9]{ x^{5} }}{\sqrt[9]{ x^{5} }}} \\=\frac{\sqrt[9]{ x^{5} }}{x}\\---------------\)
5. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-3}{4} . (\frac{-4}{3}) }= a^{1}\\\\---------------\)
6. \(\left(x^{\frac{-2}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{-2}{3} . \frac{2}{3} }= x^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ x^{4} }}=\frac{1}{\sqrt[9]{ x^{4} }}. \color{purple}{\frac{\sqrt[9]{ x^{5} }}{\sqrt[9]{ x^{5} }}} \\=\frac{\sqrt[9]{ x^{5} }}{x}\\---------------\)
7. \(\left(a^{\frac{-3}{4}}\right)^{\frac{1}{5}}\\= a^{ \frac{-3}{4} . \frac{1}{5} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
8. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-3}{5}}\\= x^{ \frac{-4}{5} . (\frac{-3}{5}) }= x^{\frac{12}{25}}\\=\sqrt[25]{ x^{12} }\\---------------\)
9. \(\left(x^{\frac{4}{3}}\right)^{\frac{-1}{6}}\\= x^{ \frac{4}{3} . (\frac{-1}{6}) }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
10. \(\left(x^{\frac{-3}{5}}\right)^{\frac{1}{6}}\\= x^{ \frac{-3}{5} . \frac{1}{6} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
11. \(\left(x^{\frac{5}{3}}\right)^{\frac{-3}{5}}\\= x^{ \frac{5}{3} . (\frac{-3}{5}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
12. \(\left(a^{\frac{-4}{5}}\right)^{1}\\= a^{ \frac{-4}{5} . 1 }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)