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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{-1}\right)^{\frac{1}{2}}\\= a^{ -1 . \frac{1}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
2. \(\left(x^{\frac{-3}{5}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-3}{5} . (\frac{-1}{4}) }= x^{\frac{3}{20}}\\=\sqrt[20]{ x^{3} }\\---------------\)
3. \(\left(y^{1}\right)^{\frac{-1}{2}}\\= y^{ 1 . (\frac{-1}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
4. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-5}{2} . (\frac{-1}{2}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
5. \(\left(x^{\frac{5}{6}}\right)^{1}\\= x^{ \frac{5}{6} . 1 }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
6. \(\left(y^{\frac{-5}{2}}\right)^{-1}\\= y^{ \frac{-5}{2} . (-1) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
7. \(\left(x^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{2} . (\frac{-2}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
8. \(\left(q^{\frac{-1}{4}}\right)^{\frac{2}{3}}\\= q^{ \frac{-1}{4} . \frac{2}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
9. \(\left(x^{\frac{-3}{2}}\right)^{1}\\= x^{ \frac{-3}{2} . 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
10. \(\left(a^{\frac{-2}{3}}\right)^{\frac{5}{3}}\\= a^{ \frac{-2}{3} . \frac{5}{3} }= a^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ a^{10} }}\\=\frac{1}{a.\sqrt[9]{ a }}=\frac{1}{a.\sqrt[9]{ a }} \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a^{2}}\\---------------\)
11. \(\left(a^{\frac{2}{3}}\right)^{-1}\\= a^{ \frac{2}{3} . (-1) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
12. \(\left(a^{\frac{-5}{4}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-5}{4} . (\frac{-5}{2}) }= a^{\frac{25}{8}}\\=\sqrt[8]{ a^{25} }=|a^{3}|.\sqrt[8]{ a }\\---------------\)