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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{2}}\right)^{-1}\\= q^{ \frac{1}{2} . (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
2. \(\left(a^{-1}\right)^{\frac{1}{2}}\\= a^{ -1 . \frac{1}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
3. \(\left(y^{\frac{2}{3}}\right)^{-1}\\= y^{ \frac{2}{3} . (-1) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
4. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{4}}\\= q^{ \frac{1}{2} . (\frac{-5}{4}) }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
5. \(\left(y^{\frac{-4}{3}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-4}{3} . (\frac{-5}{3}) }= y^{\frac{20}{9}}\\=\sqrt[9]{ y^{20} }=y^{2}.\sqrt[9]{ y^{2} }\\---------------\)
6. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-1}{3} . (\frac{-4}{5}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
7. \(\left(a^{\frac{1}{6}}\right)^{\frac{-1}{3}}\\= a^{ \frac{1}{6} . (\frac{-1}{3}) }= a^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ a }}=\frac{1}{\sqrt[18]{ a }}. \color{purple}{\frac{\sqrt[18]{ a^{17} }}{\sqrt[18]{ a^{17} }}} \\=\frac{\sqrt[18]{ a^{17} }}{|a|}\\---------------\)
8. \(\left(q^{\frac{1}{2}}\right)^{1}\\= q^{ \frac{1}{2} . 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
9. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-1}{2} . (\frac{-1}{6}) }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
10. \(\left(x^{1}\right)^{\frac{1}{4}}\\= x^{ 1 . \frac{1}{4} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
11. \(\left(q^{\frac{-1}{5}}\right)^{-1}\\= q^{ \frac{-1}{5} . (-1) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
12. \(\left(q^{-2}\right)^{-1}\\= q^{ -2 . (-1) }= q^{2}\\\\---------------\)