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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-1}{5}}\\= a^{ \frac{-2}{5} . (\frac{-1}{5}) }= a^{\frac{2}{25}}\\=\sqrt[25]{ a^{2} }\\---------------\)
2. \(\left(x^{-1}\right)^{\frac{2}{5}}\\= x^{ -1 . \frac{2}{5} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
3. \(\left(x^{\frac{1}{2}}\right)^{\frac{-5}{3}}\\= x^{ \frac{1}{2} . (\frac{-5}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
4. \(\left(a^{\frac{4}{3}}\right)^{\frac{5}{3}}\\= a^{ \frac{4}{3} . \frac{5}{3} }= a^{\frac{20}{9}}\\=\sqrt[9]{ a^{20} }=a^{2}.\sqrt[9]{ a^{2} }\\---------------\)
5. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-4}{5} . (\frac{-2}{3}) }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)
6. \(\left(y^{\frac{5}{6}}\right)^{\frac{4}{5}}\\= y^{ \frac{5}{6} . \frac{4}{5} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
7. \(\left(x^{\frac{-1}{2}}\right)^{-1}\\= x^{ \frac{-1}{2} . (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
8. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-5}{2} . (\frac{-5}{2}) }= q^{\frac{25}{4}}\\=\sqrt[4]{ q^{25} }=|q^{6}|.\sqrt[4]{ q }\\---------------\)
9. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-5}{2} . (\frac{-1}{2}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
10. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-4}{3} . (\frac{-2}{3}) }= q^{\frac{8}{9}}\\=\sqrt[9]{ q^{8} }\\---------------\)
11. \(\left(y^{1}\right)^{\frac{1}{6}}\\= y^{ 1 . \frac{1}{6} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
12. \(\left(q^{\frac{1}{6}}\right)^{-1}\\= q^{ \frac{1}{6} . (-1) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)