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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-3}{2}}\right)^{\frac{2}{5}}\\= a^{ \frac{-3}{2} . \frac{2}{5} }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
2. \(\left(x^{\frac{1}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{5} . \frac{1}{2} }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
3. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-5}{6}}\\= a^{ \frac{-2}{5} . (\frac{-5}{6}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
4. \(\left(a^{\frac{-1}{5}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{5} . \frac{1}{2} }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
5. \(\left(x^{\frac{-5}{6}}\right)^{\frac{5}{6}}\\= x^{ \frac{-5}{6} . \frac{5}{6} }= x^{\frac{-25}{36}}\\=\frac{1}{\sqrt[36]{ x^{25} }}=\frac{1}{\sqrt[36]{ x^{25} }}. \color{purple}{\frac{\sqrt[36]{ x^{11} }}{\sqrt[36]{ x^{11} }}} \\=\frac{\sqrt[36]{ x^{11} }}{|x|}\\---------------\)
6. \(\left(a^{1}\right)^{\frac{-4}{5}}\\= a^{ 1 . (\frac{-4}{5}) }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
7. \(\left(x^{\frac{4}{5}}\right)^{\frac{1}{3}}\\= x^{ \frac{4}{5} . \frac{1}{3} }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
8. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-5}{3} . (\frac{-1}{5}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
9. \(\left(a^{\frac{2}{3}}\right)^{\frac{-3}{4}}\\= a^{ \frac{2}{3} . (\frac{-3}{4}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
10. \(\left(a^{\frac{4}{5}}\right)^{\frac{-1}{4}}\\= a^{ \frac{4}{5} . (\frac{-1}{4}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
11. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-1}{4} . (\frac{-4}{5}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
12. \(\left(x^{-1}\right)^{\frac{-5}{2}}\\= x^{ -1 . (\frac{-5}{2}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)