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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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