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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{\frac{-1}{5}}\\= q^{ -1 . (\frac{-1}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
2. \(\left(x^{\frac{-3}{4}}\right)^{-1}\\= x^{ \frac{-3}{4} . (-1) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
3. \(\left(y^{\frac{-1}{6}}\right)^{\frac{1}{5}}\\= y^{ \frac{-1}{6} . \frac{1}{5} }= y^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ y }}=\frac{1}{\sqrt[30]{ y }}. \color{purple}{\frac{\sqrt[30]{ y^{29} }}{\sqrt[30]{ y^{29} }}} \\=\frac{\sqrt[30]{ y^{29} }}{|y|}\\---------------\)
4. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{3}}\\= a^{ \frac{5}{6} . \frac{1}{3} }= a^{\frac{5}{18}}\\=\sqrt[18]{ a^{5} }\\---------------\)
5. \(\left(y^{-1}\right)^{-2}\\= y^{ -1 . (-2) }= y^{2}\\\\---------------\)
6. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-3}{4} . (\frac{-1}{4}) }= y^{\frac{3}{16}}\\=\sqrt[16]{ y^{3} }\\---------------\)
7. \(\left(q^{-1}\right)^{\frac{-5}{3}}\\= q^{ -1 . (\frac{-5}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
8. \(\left(x^{-1}\right)^{\frac{5}{3}}\\= x^{ -1 . \frac{5}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
9. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-5}{6} . (\frac{-5}{6}) }= y^{\frac{25}{36}}\\=\sqrt[36]{ y^{25} }\\---------------\)
10. \(\left(a^{\frac{-5}{6}}\right)^{-1}\\= a^{ \frac{-5}{6} . (-1) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
11. \(\left(y^{\frac{5}{2}}\right)^{1}\\= y^{ \frac{5}{2} . 1 }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
12. \(\left(a^{\frac{1}{2}}\right)^{-1}\\= a^{ \frac{1}{2} . (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)