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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-1}{3} . (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
2. \(\left(x^{\frac{-1}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{-1}{3} . \frac{2}{3} }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
3. \(\left(y^{\frac{-1}{3}}\right)^{\frac{2}{5}}\\= y^{ \frac{-1}{3} . \frac{2}{5} }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
4. \(\left(q^{\frac{4}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{4}{5} . (\frac{-1}{5}) }= q^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ q^{4} }}=\frac{1}{\sqrt[25]{ q^{4} }}. \color{purple}{\frac{\sqrt[25]{ q^{21} }}{\sqrt[25]{ q^{21} }}} \\=\frac{\sqrt[25]{ q^{21} }}{q}\\---------------\)
5. \(\left(x^{\frac{-1}{3}}\right)^{1}\\= x^{ \frac{-1}{3} . 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\left(y^{\frac{5}{2}}\right)^{\frac{-5}{6}}\\= y^{ \frac{5}{2} . (\frac{-5}{6}) }= y^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ y^{25} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y }}=\frac{1}{|y^{2}|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{3}|}\\---------------\)
7. \(\left(x^{1}\right)^{1}\\= x^{ 1 . 1 }= x^{1}\\\\---------------\)
8. \(\left(q^{\frac{1}{6}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{6} . \frac{1}{2} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
9. \(\left(a^{\frac{1}{2}}\right)^{1}\\= a^{ \frac{1}{2} . 1 }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
10. \(\left(a^{\frac{1}{3}}\right)^{\frac{-5}{2}}\\= a^{ \frac{1}{3} . (\frac{-5}{2}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
11. \(\left(a^{\frac{-4}{3}}\right)^{\frac{2}{5}}\\= a^{ \frac{-4}{3} . \frac{2}{5} }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
12. \(\left(y^{\frac{2}{3}}\right)^{\frac{5}{6}}\\= y^{ \frac{2}{3} . \frac{5}{6} }= y^{\frac{5}{9}}\\=\sqrt[9]{ y^{5} }\\---------------\)