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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{\frac{-3}{5}}\\= q^{ -1 . (\frac{-3}{5}) }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
2. \(\left(y^{\frac{-4}{5}}\right)^{\frac{2}{3}}\\= y^{ \frac{-4}{5} . \frac{2}{3} }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
3. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-2}{3} . (\frac{-3}{4}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
4. \(\left(x^{\frac{1}{6}}\right)^{\frac{5}{3}}\\= x^{ \frac{1}{6} . \frac{5}{3} }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)
5. \(\left(y^{\frac{5}{2}}\right)^{\frac{4}{3}}\\= y^{ \frac{5}{2} . \frac{4}{3} }= y^{\frac{10}{3}}\\=\sqrt[3]{ y^{10} }=y^{3}.\sqrt[3]{ y }\\---------------\)
6. \(\left(y^{\frac{2}{5}}\right)^{\frac{-3}{5}}\\= y^{ \frac{2}{5} . (\frac{-3}{5}) }= y^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ y^{6} }}=\frac{1}{\sqrt[25]{ y^{6} }}. \color{purple}{\frac{\sqrt[25]{ y^{19} }}{\sqrt[25]{ y^{19} }}} \\=\frac{\sqrt[25]{ y^{19} }}{y}\\---------------\)
7. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-3}{5} . (\frac{-3}{2}) }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
8. \(\left(y^{\frac{2}{3}}\right)^{\frac{4}{5}}\\= y^{ \frac{2}{3} . \frac{4}{5} }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)
9. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-2}{5}}\\= a^{ \frac{-2}{3} . (\frac{-2}{5}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
10. \(\left(y^{-1}\right)^{-1}\\= y^{ -1 . (-1) }= y^{1}\\\\---------------\)
11. \(\left(q^{\frac{-1}{4}}\right)^{1}\\= q^{ \frac{-1}{4} . 1 }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
12. \(\left(q^{\frac{5}{4}}\right)^{\frac{-5}{6}}\\= q^{ \frac{5}{4} . (\frac{-5}{6}) }= q^{\frac{-25}{24}}\\=\frac{1}{\sqrt[24]{ q^{25} }}\\=\frac{1}{|q|.\sqrt[24]{ q }}=\frac{1}{|q|.\sqrt[24]{ q }} \color{purple}{\frac{\sqrt[24]{ q^{23} }}{\sqrt[24]{ q^{23} }}} \\=\frac{\sqrt[24]{ q^{23} }}{|q^{2}|}\\---------------\)