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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{6}}\\= a^{ \frac{1}{3} . \frac{1}{6} }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
2. \(\left(x^{1}\right)^{\frac{3}{5}}\\= x^{ 1 . \frac{3}{5} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
3. \(\left(x^{\frac{5}{3}}\right)^{\frac{-3}{4}}\\= x^{ \frac{5}{3} . (\frac{-3}{4}) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
4. \(\left(y^{\frac{-1}{3}}\right)^{\frac{5}{2}}\\= y^{ \frac{-1}{3} . \frac{5}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
5. \(\left(a^{\frac{-2}{5}}\right)^{-1}\\= a^{ \frac{-2}{5} . (-1) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
6. \(\left(y^{\frac{-1}{2}}\right)^{\frac{5}{2}}\\= y^{ \frac{-1}{2} . \frac{5}{2} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
7. \(\left(q^{\frac{-3}{5}}\right)^{1}\\= q^{ \frac{-3}{5} . 1 }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
8. \(\left(x^{-1}\right)^{\frac{-2}{3}}\\= x^{ -1 . (\frac{-2}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
9. \(\left(x^{-2}\right)^{\frac{-1}{2}}\\= x^{ -2 . (\frac{-1}{2}) }= x^{1}\\\\---------------\)
10. \(\left(x^{\frac{2}{5}}\right)^{\frac{-2}{5}}\\= x^{ \frac{2}{5} . (\frac{-2}{5}) }= x^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ x^{4} }}=\frac{1}{\sqrt[25]{ x^{4} }}. \color{purple}{\frac{\sqrt[25]{ x^{21} }}{\sqrt[25]{ x^{21} }}} \\=\frac{\sqrt[25]{ x^{21} }}{x}\\---------------\)
11. \(\left(x^{\frac{1}{6}}\right)^{\frac{-2}{5}}\\= x^{ \frac{1}{6} . (\frac{-2}{5}) }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
12. \(\left(x^{\frac{-5}{4}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-5}{4} . (\frac{-2}{3}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)