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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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