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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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