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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{2}}\right)^{\frac{-4}{3}}\\= y^{ \frac{1}{2} . (\frac{-4}{3}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
2. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-5}{6} . (\frac{-5}{2}) }= q^{\frac{25}{12}}\\=\sqrt[12]{ q^{25} }=|q^{2}|.\sqrt[12]{ q }\\---------------\)
3. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-4}{3} . (\frac{-1}{3}) }= q^{\frac{4}{9}}\\=\sqrt[9]{ q^{4} }\\---------------\)
4. \(\left(a^{\frac{-3}{2}}\right)^{\frac{-2}{5}}\\= a^{ \frac{-3}{2} . (\frac{-2}{5}) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
5. \(\left(x^{\frac{-3}{4}}\right)^{\frac{1}{4}}\\= x^{ \frac{-3}{4} . \frac{1}{4} }= x^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ x^{3} }}=\frac{1}{\sqrt[16]{ x^{3} }}. \color{purple}{\frac{\sqrt[16]{ x^{13} }}{\sqrt[16]{ x^{13} }}} \\=\frac{\sqrt[16]{ x^{13} }}{|x|}\\---------------\)
6. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-2}{3} . (\frac{-4}{5}) }= a^{\frac{8}{15}}\\=\sqrt[15]{ a^{8} }\\---------------\)
7. \(\left(x^{1}\right)^{\frac{-1}{2}}\\= x^{ 1 . (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\left(a^{\frac{-5}{4}}\right)^{1}\\= a^{ \frac{-5}{4} . 1 }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
9. \(\left(x^{-1}\right)^{\frac{-5}{6}}\\= x^{ -1 . (\frac{-5}{6}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
10. \(\left(x^{-1}\right)^{\frac{-3}{5}}\\= x^{ -1 . (\frac{-3}{5}) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
11. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-2}{5}}\\= y^{ \frac{-2}{3} . (\frac{-2}{5}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
12. \(\left(q^{\frac{5}{4}}\right)^{-2}\\= q^{ \frac{5}{4} . (-2) }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)