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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{1}\right)^{\frac{-1}{6}}\\= x^{ 1 . (\frac{-1}{6}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
2. \(\left(x^{\frac{1}{3}}\right)^{\frac{-2}{5}}\\= x^{ \frac{1}{3} . (\frac{-2}{5}) }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
3. \(\left(a^{\frac{4}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{4}{5} . \frac{1}{3} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
4. \(\left(x^{-2}\right)^{\frac{-5}{6}}\\= x^{ -2 . (\frac{-5}{6}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
5. \(\left(q^{\frac{-1}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{-1}{3} . \frac{2}{3} }= q^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ q^{2} }}=\frac{1}{\sqrt[9]{ q^{2} }}. \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q}\\---------------\)
6. \(\left(a^{\frac{-1}{6}}\right)^{\frac{1}{6}}\\= a^{ \frac{-1}{6} . \frac{1}{6} }= a^{\frac{-1}{36}}\\=\frac{1}{\sqrt[36]{ a }}=\frac{1}{\sqrt[36]{ a }}. \color{purple}{\frac{\sqrt[36]{ a^{35} }}{\sqrt[36]{ a^{35} }}} \\=\frac{\sqrt[36]{ a^{35} }}{|a|}\\---------------\)
7. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{2} . (\frac{-1}{2}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
8. \(\left(y^{\frac{-3}{4}}\right)^{\frac{5}{2}}\\= y^{ \frac{-3}{4} . \frac{5}{2} }= y^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ y^{15} }}\\=\frac{1}{|y|.\sqrt[8]{ y^{7} }}=\frac{1}{|y|.\sqrt[8]{ y^{7} }} \color{purple}{\frac{\sqrt[8]{ y }}{\sqrt[8]{ y }}} \\=\frac{\sqrt[8]{ y }}{|y^{2}|}\\---------------\)
9. \(\left(x^{-1}\right)^{\frac{1}{6}}\\= x^{ -1 . \frac{1}{6} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
10. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-1}{4} . (\frac{-1}{5}) }= x^{\frac{1}{20}}\\=\sqrt[20]{ x }\\---------------\)
11. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-5}{3} . (\frac{-3}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
12. \(\left(y^{1}\right)^{\frac{-3}{4}}\\= y^{ 1 . (\frac{-3}{4}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)