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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{3}}\right)^{\frac{1}{5}}\\= x^{ \frac{5}{3} . \frac{1}{5} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
2. \(\left(q^{1}\right)^{2}\\= q^{ 1 . 2 }= q^{2}\\\\---------------\)
3. \(\left(y^{\frac{1}{6}}\right)^{\frac{-1}{3}}\\= y^{ \frac{1}{6} . (\frac{-1}{3}) }= y^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ y }}=\frac{1}{\sqrt[18]{ y }}. \color{purple}{\frac{\sqrt[18]{ y^{17} }}{\sqrt[18]{ y^{17} }}} \\=\frac{\sqrt[18]{ y^{17} }}{|y|}\\---------------\)
4. \(\left(x^{\frac{5}{3}}\right)^{\frac{-5}{4}}\\= x^{ \frac{5}{3} . (\frac{-5}{4}) }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
5. \(\left(q^{\frac{5}{6}}\right)^{1}\\= q^{ \frac{5}{6} . 1 }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
6. \(\left(q^{\frac{-5}{3}}\right)^{\frac{5}{2}}\\= q^{ \frac{-5}{3} . \frac{5}{2} }= q^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ q^{25} }}\\=\frac{1}{|q^{4}|.\sqrt[6]{ q }}=\frac{1}{|q^{4}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{5}|}\\---------------\)
7. \(\left(x^{\frac{2}{3}}\right)^{\frac{4}{3}}\\= x^{ \frac{2}{3} . \frac{4}{3} }= x^{\frac{8}{9}}\\=\sqrt[9]{ x^{8} }\\---------------\)
8. \(\left(y^{-1}\right)^{\frac{3}{5}}\\= y^{ -1 . \frac{3}{5} }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
9. \(\left(y^{\frac{1}{5}}\right)^{1}\\= y^{ \frac{1}{5} . 1 }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
10. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-4}{3} . (\frac{-4}{5}) }= a^{\frac{16}{15}}\\=\sqrt[15]{ a^{16} }=a.\sqrt[15]{ a }\\---------------\)
11. \(\left(a^{\frac{3}{5}}\right)^{\frac{5}{6}}\\= a^{ \frac{3}{5} . \frac{5}{6} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\left(q^{-1}\right)^{\frac{1}{3}}\\= q^{ -1 . \frac{1}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)