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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= x^{ \frac{-1}{2} . \frac{2}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
2. \(\left(x^{1}\right)^{\frac{-4}{3}}\\= x^{ 1 . (\frac{-4}{3}) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
3. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-2}{5}}\\= y^{ \frac{-3}{5} . (\frac{-2}{5}) }= y^{\frac{6}{25}}\\=\sqrt[25]{ y^{6} }\\---------------\)
4. \(\left(y^{-1}\right)^{\frac{1}{3}}\\= y^{ -1 . \frac{1}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
5. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-2}{3} . (\frac{-1}{2}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
6. \(\left(y^{-1}\right)^{\frac{-5}{6}}\\= y^{ -1 . (\frac{-5}{6}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
7. \(\left(x^{\frac{3}{2}}\right)^{\frac{-1}{6}}\\= x^{ \frac{3}{2} . (\frac{-1}{6}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
8. \(\left(x^{\frac{-4}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{-4}{5} . \frac{1}{2} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
9. \(\left(y^{\frac{-1}{2}}\right)^{1}\\= y^{ \frac{-1}{2} . 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
10. \(\left(y^{\frac{5}{6}}\right)^{\frac{-5}{3}}\\= y^{ \frac{5}{6} . (\frac{-5}{3}) }= y^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[18]{ y^{7} }}=\frac{1}{|y|.\sqrt[18]{ y^{7} }} \color{purple}{\frac{\sqrt[18]{ y^{11} }}{\sqrt[18]{ y^{11} }}} \\=\frac{\sqrt[18]{ y^{11} }}{|y^{2}|}\\---------------\)
11. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-1}{3} . (\frac{-5}{6}) }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)
12. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-5}{6} . (\frac{-1}{2}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)