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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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