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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-3}{2}}\right)^{\frac{-5}{6}}\\= q^{ \frac{-3}{2} . (\frac{-5}{6}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
2. \(\left(q^{\frac{-5}{6}}\right)^{\frac{1}{6}}\\= q^{ \frac{-5}{6} . \frac{1}{6} }= q^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ q^{5} }}=\frac{1}{\sqrt[36]{ q^{5} }}. \color{purple}{\frac{\sqrt[36]{ q^{31} }}{\sqrt[36]{ q^{31} }}} \\=\frac{\sqrt[36]{ q^{31} }}{|q|}\\---------------\)
3. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-1}{6} . (\frac{-1}{3}) }= y^{\frac{1}{18}}\\=\sqrt[18]{ y }\\---------------\)
4. \(\left(x^{\frac{1}{3}}\right)^{1}\\= x^{ \frac{1}{3} . 1 }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
5. \(\left(y^{\frac{-1}{6}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{6} . \frac{1}{2} }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
6. \(\left(x^{-2}\right)^{\frac{-1}{2}}\\= x^{ -2 . (\frac{-1}{2}) }= x^{1}\\\\---------------\)
7. \(\left(a^{\frac{2}{3}}\right)^{\frac{-4}{5}}\\= a^{ \frac{2}{3} . (\frac{-4}{5}) }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
8. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-2}{5}}\\= x^{ \frac{-2}{3} . (\frac{-2}{5}) }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
9. \(\left(a^{\frac{5}{6}}\right)^{1}\\= a^{ \frac{5}{6} . 1 }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
10. \(\left(a^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= a^{ \frac{1}{2} . (\frac{-3}{4}) }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)
11. \(\left(a^{\frac{2}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{2}{5} . (\frac{-3}{5}) }= a^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ a^{6} }}=\frac{1}{\sqrt[25]{ a^{6} }}. \color{purple}{\frac{\sqrt[25]{ a^{19} }}{\sqrt[25]{ a^{19} }}} \\=\frac{\sqrt[25]{ a^{19} }}{a}\\---------------\)
12. \(\left(x^{\frac{-5}{2}}\right)^{1}\\= x^{ \frac{-5}{2} . 1 }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)