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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{-2}\right)^{\frac{5}{4}}\\= x^{ -2 . \frac{5}{4} }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
2. \(\left(q^{\frac{-1}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{5} . \frac{1}{3} }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
3. \(\left(x^{\frac{1}{4}}\right)^{\frac{-3}{2}}\\= x^{ \frac{1}{4} . (\frac{-3}{2}) }= x^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ x^{3} }}=\frac{1}{\sqrt[8]{ x^{3} }}. \color{purple}{\frac{\sqrt[8]{ x^{5} }}{\sqrt[8]{ x^{5} }}} \\=\frac{\sqrt[8]{ x^{5} }}{|x|}\\---------------\)
4. \(\left(q^{\frac{3}{2}}\right)^{\frac{3}{5}}\\= q^{ \frac{3}{2} . \frac{3}{5} }= q^{\frac{9}{10}}\\=\sqrt[10]{ q^{9} }\\---------------\)
5. \(\left(a^{\frac{-5}{4}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-5}{4} . (\frac{-1}{6}) }= a^{\frac{5}{24}}\\=\sqrt[24]{ a^{5} }\\---------------\)
6. \(\left(a^{\frac{3}{5}}\right)^{1}\\= a^{ \frac{3}{5} . 1 }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
7. \(\left(a^{\frac{1}{6}}\right)^{-2}\\= a^{ \frac{1}{6} . (-2) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
8. \(\left(y^{\frac{3}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{3}{5} . \frac{1}{3} }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
9. \(\left(q^{\frac{-4}{5}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-4}{5} . (\frac{-2}{5}) }= q^{\frac{8}{25}}\\=\sqrt[25]{ q^{8} }\\---------------\)
10. \(\left(q^{\frac{1}{4}}\right)^{\frac{-3}{4}}\\= q^{ \frac{1}{4} . (\frac{-3}{4}) }= q^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ q^{3} }}=\frac{1}{\sqrt[16]{ q^{3} }}. \color{purple}{\frac{\sqrt[16]{ q^{13} }}{\sqrt[16]{ q^{13} }}} \\=\frac{\sqrt[16]{ q^{13} }}{|q|}\\---------------\)
11. \(\left(x^{\frac{-3}{5}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-3}{5} . (\frac{-5}{6}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\left(a^{\frac{3}{4}}\right)^{\frac{1}{6}}\\= a^{ \frac{3}{4} . \frac{1}{6} }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)