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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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