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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-1}{3} . (\frac{-5}{2}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
2. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{2} . \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
3. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{2} . (\frac{-2}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
4. \(\left(x^{-2}\right)^{\frac{5}{4}}\\= x^{ -2 . \frac{5}{4} }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
5. \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{-2}{3} . \frac{1}{5} }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
6. \(\left(y^{\frac{1}{5}}\right)^{\frac{-4}{5}}\\= y^{ \frac{1}{5} . (\frac{-4}{5}) }= y^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ y^{4} }}=\frac{1}{\sqrt[25]{ y^{4} }}. \color{purple}{\frac{\sqrt[25]{ y^{21} }}{\sqrt[25]{ y^{21} }}} \\=\frac{\sqrt[25]{ y^{21} }}{y}\\---------------\)
7. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-5}{6} . (\frac{-5}{3}) }= q^{\frac{25}{18}}\\=\sqrt[18]{ q^{25} }=|q|.\sqrt[18]{ q^{7} }\\---------------\)
8. \(\left(a^{2}\right)^{\frac{-2}{5}}\\= a^{ 2 . (\frac{-2}{5}) }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
9. \(\left(a^{\frac{4}{5}}\right)^{\frac{5}{6}}\\= a^{ \frac{4}{5} . \frac{5}{6} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
10. \(\left(x^{\frac{5}{6}}\right)^{\frac{-2}{5}}\\= x^{ \frac{5}{6} . (\frac{-2}{5}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
11. \(\left(x^{\frac{5}{6}}\right)^{\frac{1}{6}}\\= x^{ \frac{5}{6} . \frac{1}{6} }= x^{\frac{5}{36}}\\=\sqrt[36]{ x^{5} }\\---------------\)
12. \(\left(a^{\frac{-5}{4}}\right)^{1}\\= a^{ \frac{-5}{4} . 1 }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)