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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-5}{6}}\right)^{\frac{1}{6}}\\= a^{ \frac{-5}{6} . \frac{1}{6} }= a^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ a^{5} }}=\frac{1}{\sqrt[36]{ a^{5} }}. \color{purple}{\frac{\sqrt[36]{ a^{31} }}{\sqrt[36]{ a^{31} }}} \\=\frac{\sqrt[36]{ a^{31} }}{|a|}\\---------------\)
2. \(\left(y^{-1}\right)^{\frac{3}{5}}\\= y^{ -1 . \frac{3}{5} }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
3. \(\left(x^{1}\right)^{\frac{1}{4}}\\= x^{ 1 . \frac{1}{4} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
4. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{2} . \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
5. \(\left(x^{-1}\right)^{-1}\\= x^{ -1 . (-1) }= x^{1}\\\\---------------\)
6. \(\left(x^{-1}\right)^{\frac{3}{2}}\\= x^{ -1 . \frac{3}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
7. \(\left(a^{\frac{1}{6}}\right)^{-2}\\= a^{ \frac{1}{6} . (-2) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
8. \(\left(y^{\frac{5}{2}}\right)^{\frac{2}{5}}\\= y^{ \frac{5}{2} . \frac{2}{5} }= y^{1}\\\\---------------\)
9. \(\left(q^{\frac{5}{4}}\right)^{\frac{-1}{2}}\\= q^{ \frac{5}{4} . (\frac{-1}{2}) }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
10. \(\left(y^{\frac{1}{2}}\right)^{\frac{-5}{6}}\\= y^{ \frac{1}{2} . (\frac{-5}{6}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
11. \(\left(y^{1}\right)^{\frac{3}{5}}\\= y^{ 1 . \frac{3}{5} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
12. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-3}{5} . (\frac{-2}{3}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)