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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{1}\right)^{\frac{-1}{2}}\\= x^{ 1 . (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
2. \(\left(a^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{2} . \frac{2}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
3. \(\left(y^{1}\right)^{\frac{-4}{3}}\\= y^{ 1 . (\frac{-4}{3}) }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
4. \(\left(y^{\frac{1}{6}}\right)^{\frac{1}{5}}\\= y^{ \frac{1}{6} . \frac{1}{5} }= y^{\frac{1}{30}}\\=\sqrt[30]{ y }\\---------------\)
5. \(\left(y^{\frac{-3}{5}}\right)^{1}\\= y^{ \frac{-3}{5} . 1 }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
6. \(\left(y^{\frac{3}{4}}\right)^{\frac{-3}{2}}\\= y^{ \frac{3}{4} . (\frac{-3}{2}) }= y^{\frac{-9}{8}}\\=\frac{1}{\sqrt[8]{ y^{9} }}\\=\frac{1}{|y|.\sqrt[8]{ y }}=\frac{1}{|y|.\sqrt[8]{ y }} \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y^{2}|}\\---------------\)
7. \(\left(x^{\frac{-1}{3}}\right)^{-1}\\= x^{ \frac{-1}{3} . (-1) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
8. \(\left(y^{1}\right)^{\frac{-1}{4}}\\= y^{ 1 . (\frac{-1}{4}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
9. \(\left(x^{\frac{1}{6}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{6} . (\frac{-2}{3}) }= x^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ x }}=\frac{1}{\sqrt[9]{ x }}. \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x}\\---------------\)
10. \(\left(a^{\frac{4}{5}}\right)^{1}\\= a^{ \frac{4}{5} . 1 }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
11. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-4}{3} . (\frac{-1}{2}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
12. \(\left(y^{\frac{-1}{2}}\right)^{-2}\\= y^{ \frac{-1}{2} . (-2) }= y^{1}\\\\---------------\)