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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{6}}\right)^{\frac{-2}{5}}\\= x^{ \frac{-1}{6} . (\frac{-2}{5}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
2. \(\left(y^{\frac{1}{2}}\right)^{-2}\\= y^{ \frac{1}{2} . (-2) }= y^{-1}\\=\frac{1}{y}\\---------------\)
3. \(\left(y^{\frac{5}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{5}{3} . \frac{2}{3} }= y^{\frac{10}{9}}\\=\sqrt[9]{ y^{10} }=y.\sqrt[9]{ y }\\---------------\)
4. \(\left(a^{\frac{1}{3}}\right)^{-1}\\= a^{ \frac{1}{3} . (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\left(a^{\frac{-2}{3}}\right)^{\frac{2}{5}}\\= a^{ \frac{-2}{3} . \frac{2}{5} }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
6. \(\left(q^{-1}\right)^{-1}\\= q^{ -1 . (-1) }= q^{1}\\\\---------------\)
7. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{2} . (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
8. \(\left(y^{-1}\right)^{\frac{2}{3}}\\= y^{ -1 . \frac{2}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
9. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)
10. \(\left(y^{\frac{-1}{5}}\right)^{\frac{4}{5}}\\= y^{ \frac{-1}{5} . \frac{4}{5} }= y^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ y^{4} }}=\frac{1}{\sqrt[25]{ y^{4} }}. \color{purple}{\frac{\sqrt[25]{ y^{21} }}{\sqrt[25]{ y^{21} }}} \\=\frac{\sqrt[25]{ y^{21} }}{y}\\---------------\)
11. \(\left(x^{\frac{-5}{2}}\right)^{1}\\= x^{ \frac{-5}{2} . 1 }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
12. \(\left(a^{2}\right)^{\frac{1}{2}}\\= a^{ 2 . \frac{1}{2} }= a^{1}\\\\---------------\)