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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{2}}\right)^{1}\\= a^{ \frac{1}{2} . 1 }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
2. \(\left(x^{\frac{1}{3}}\right)^{\frac{1}{6}}\\= x^{ \frac{1}{3} . \frac{1}{6} }= x^{\frac{1}{18}}\\=\sqrt[18]{ x }\\---------------\)
3. \(\left(q^{\frac{-1}{2}}\right)^{-1}\\= q^{ \frac{-1}{2} . (-1) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
4. \(\left(a^{\frac{-3}{2}}\right)^{\frac{1}{3}}\\= a^{ \frac{-3}{2} . \frac{1}{3} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
5. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-5}{2}}\\= y^{ \frac{-3}{5} . (\frac{-5}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
6. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-2}{5}}\\= y^{ \frac{-1}{3} . (\frac{-2}{5}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
7. \(\left(a^{\frac{-2}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{-2}{5} . \frac{1}{3} }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
8. \(\left(a^{\frac{1}{5}}\right)^{\frac{-1}{6}}\\= a^{ \frac{1}{5} . (\frac{-1}{6}) }= a^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ a }}=\frac{1}{\sqrt[30]{ a }}. \color{purple}{\frac{\sqrt[30]{ a^{29} }}{\sqrt[30]{ a^{29} }}} \\=\frac{\sqrt[30]{ a^{29} }}{|a|}\\---------------\)
9. \(\left(q^{\frac{-5}{6}}\right)^{\frac{1}{5}}\\= q^{ \frac{-5}{6} . \frac{1}{5} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
10. \(\left(x^{\frac{-2}{3}}\right)^{-1}\\= x^{ \frac{-2}{3} . (-1) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
11. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-5}{2} . (\frac{-1}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
12. \(\left(q^{\frac{-1}{3}}\right)^{1}\\= q^{ \frac{-1}{3} . 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)