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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{5}}\right)^{\frac{1}{6}}\\= x^{ \frac{1}{5} . \frac{1}{6} }= x^{\frac{1}{30}}\\=\sqrt[30]{ x }\\---------------\)
2. \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{3}}\\= a^{ \frac{1}{6} . \frac{1}{3} }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
3. \(\left(a^{1}\right)^{1}\\= a^{ 1 . 1 }= a^{1}\\\\---------------\)
4. \(\left(a^{\frac{5}{6}}\right)^{\frac{-2}{5}}\\= a^{ \frac{5}{6} . (\frac{-2}{5}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\left(y^{\frac{4}{3}}\right)^{\frac{1}{6}}\\= y^{ \frac{4}{3} . \frac{1}{6} }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
6. \(\left(a^{\frac{1}{6}}\right)^{\frac{-4}{5}}\\= a^{ \frac{1}{6} . (\frac{-4}{5}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
7. \(\left(a^{\frac{3}{4}}\right)^{\frac{4}{5}}\\= a^{ \frac{3}{4} . \frac{4}{5} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
8. \(\left(x^{\frac{5}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{5}{4} . \frac{1}{2} }= x^{\frac{5}{8}}\\=\sqrt[8]{ x^{5} }\\---------------\)
9. \(\left(y^{1}\right)^{-1}\\= y^{ 1 . (-1) }= y^{-1}\\=\frac{1}{y}\\---------------\)
10. \(\left(a^{-1}\right)^{1}\\= a^{ -1 . 1 }= a^{-1}\\=\frac{1}{a}\\---------------\)
11. \(\left(y^{\frac{-3}{5}}\right)^{1}\\= y^{ \frac{-3}{5} . 1 }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
12. \(\left(y^{\frac{-5}{2}}\right)^{1}\\= y^{ \frac{-5}{2} . 1 }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)