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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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