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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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