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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{5}}\right)^{\frac{2}{5}}\\= a^{ \frac{1}{5} . \frac{2}{5} }= a^{\frac{2}{25}}\\=\sqrt[25]{ a^{2} }\\---------------\)
2. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-2}{5} . (\frac{-3}{5}) }= a^{\frac{6}{25}}\\=\sqrt[25]{ a^{6} }\\---------------\)
3. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-4}{3}}\\= y^{ \frac{-3}{5} . (\frac{-4}{3}) }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
4. \(\left(a^{\frac{1}{3}}\right)^{\frac{5}{6}}\\= a^{ \frac{1}{3} . \frac{5}{6} }= a^{\frac{5}{18}}\\=\sqrt[18]{ a^{5} }\\---------------\)
5. \(\left(x^{\frac{-4}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{-4}{5} . \frac{2}{3} }= x^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ x^{8} }}=\frac{1}{\sqrt[15]{ x^{8} }}. \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x}\\---------------\)
6. \(\left(a^{\frac{-2}{3}}\right)^{\frac{3}{4}}\\= a^{ \frac{-2}{3} . \frac{3}{4} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
7. \(\left(a^{\frac{1}{6}}\right)^{\frac{-3}{2}}\\= a^{ \frac{1}{6} . (\frac{-3}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
8. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-4}{5} . (\frac{-5}{6}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
9. \(\left(a^{-1}\right)^{\frac{-1}{2}}\\= a^{ -1 . (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
10. \(\left(x^{\frac{-4}{3}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-4}{3} . (\frac{-1}{4}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
11. \(\left(y^{-1}\right)^{\frac{-1}{4}}\\= y^{ -1 . (\frac{-1}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
12. \(\left(y^{\frac{5}{4}}\right)^{\frac{2}{5}}\\= y^{ \frac{5}{4} . \frac{2}{5} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)