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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{1}\right)^{\frac{-3}{2}}\\= y^{ 1 . (\frac{-3}{2}) }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
2. \(\left(x^{\frac{3}{4}}\right)^{\frac{-1}{2}}\\= x^{ \frac{3}{4} . (\frac{-1}{2}) }= x^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ x^{3} }}=\frac{1}{\sqrt[8]{ x^{3} }}. \color{purple}{\frac{\sqrt[8]{ x^{5} }}{\sqrt[8]{ x^{5} }}} \\=\frac{\sqrt[8]{ x^{5} }}{|x|}\\---------------\)
3. \(\left(q^{-1}\right)^{\frac{-1}{6}}\\= q^{ -1 . (\frac{-1}{6}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
4. \(\left(a^{\frac{1}{6}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{6} . (\frac{-1}{2}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
5. \(\left(y^{\frac{4}{5}}\right)^{\frac{-5}{4}}\\= y^{ \frac{4}{5} . (\frac{-5}{4}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
6. \(\left(q^{\frac{-5}{3}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-5}{3} . (\frac{-1}{4}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
7. \(\left(a^{\frac{-1}{6}}\right)^{\frac{1}{6}}\\= a^{ \frac{-1}{6} . \frac{1}{6} }= a^{\frac{-1}{36}}\\=\frac{1}{\sqrt[36]{ a }}=\frac{1}{\sqrt[36]{ a }}. \color{purple}{\frac{\sqrt[36]{ a^{35} }}{\sqrt[36]{ a^{35} }}} \\=\frac{\sqrt[36]{ a^{35} }}{|a|}\\---------------\)
8. \(\left(y^{\frac{1}{6}}\right)^{\frac{2}{3}}\\= y^{ \frac{1}{6} . \frac{2}{3} }= y^{\frac{1}{9}}\\=\sqrt[9]{ y }\\---------------\)
9. \(\left(a^{\frac{-2}{5}}\right)^{1}\\= a^{ \frac{-2}{5} . 1 }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
10. \(\left(x^{\frac{-5}{2}}\right)^{1}\\= x^{ \frac{-5}{2} . 1 }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
11. \(\left(y^{\frac{5}{2}}\right)^{\frac{-4}{5}}\\= y^{ \frac{5}{2} . (\frac{-4}{5}) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-5}{6}}\\= q^{ \frac{-1}{2} . (\frac{-5}{6}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)