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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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