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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{2}}\right)^{\frac{-5}{6}}\\= x^{ \frac{1}{2} . (\frac{-5}{6}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
2. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-1}{2} . (\frac{-2}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
3. \(\left(a^{\frac{-4}{5}}\right)^{\frac{5}{6}}\\= a^{ \frac{-4}{5} . \frac{5}{6} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
4. \(\left(y^{2}\right)^{-1}\\= y^{ 2 . (-1) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
5. \(\left(x^{\frac{5}{4}}\right)^{\frac{1}{5}}\\= x^{ \frac{5}{4} . \frac{1}{5} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
6. \(\left(a^{\frac{-2}{3}}\right)^{\frac{4}{3}}\\= a^{ \frac{-2}{3} . \frac{4}{3} }= a^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ a^{8} }}=\frac{1}{\sqrt[9]{ a^{8} }}. \color{purple}{\frac{\sqrt[9]{ a }}{\sqrt[9]{ a }}} \\=\frac{\sqrt[9]{ a }}{a}\\---------------\)
7. \(\left(a^{\frac{1}{2}}\right)^{-1}\\= a^{ \frac{1}{2} . (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
8. \(\left(a^{-1}\right)^{\frac{3}{2}}\\= a^{ -1 . \frac{3}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
9. \(\left(y^{\frac{2}{3}}\right)^{\frac{-3}{2}}\\= y^{ \frac{2}{3} . (\frac{-3}{2}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
10. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)
11. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-5}{6} . (\frac{-1}{3}) }= y^{\frac{5}{18}}\\=\sqrt[18]{ y^{5} }\\---------------\)
12. \(\left(y^{\frac{2}{5}}\right)^{\frac{-1}{5}}\\= y^{ \frac{2}{5} . (\frac{-1}{5}) }= y^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ y^{2} }}=\frac{1}{\sqrt[25]{ y^{2} }}. \color{purple}{\frac{\sqrt[25]{ y^{23} }}{\sqrt[25]{ y^{23} }}} \\=\frac{\sqrt[25]{ y^{23} }}{y}\\---------------\)