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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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