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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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