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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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