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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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