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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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