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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-2}{3}}\right)^{\frac{1}{6}}\\= q^{ \frac{-2}{3} . \frac{1}{6} }= q^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ q }}=\frac{1}{\sqrt[9]{ q }}. \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q}\\---------------\)
2. \(\left(q^{\frac{2}{3}}\right)^{\frac{5}{6}}\\= q^{ \frac{2}{3} . \frac{5}{6} }= q^{\frac{5}{9}}\\=\sqrt[9]{ q^{5} }\\---------------\)
3. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-3}{5} . (\frac{-3}{4}) }= q^{\frac{9}{20}}\\=\sqrt[20]{ q^{9} }\\---------------\)
4. \(\left(q^{\frac{-5}{3}}\right)^{\frac{4}{3}}\\= q^{ \frac{-5}{3} . \frac{4}{3} }= q^{\frac{-20}{9}}\\=\frac{1}{\sqrt[9]{ q^{20} }}\\=\frac{1}{q^{2}.\sqrt[9]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[9]{ q^{2} }} \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q^{3}}\\---------------\)
5. \(\left(y^{\frac{1}{4}}\right)^{\frac{-1}{5}}\\= y^{ \frac{1}{4} . (\frac{-1}{5}) }= y^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ y }}=\frac{1}{\sqrt[20]{ y }}. \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y|}\\---------------\)
6. \(\left(x^{\frac{-2}{5}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-2}{5} . (\frac{-4}{5}) }= x^{\frac{8}{25}}\\=\sqrt[25]{ x^{8} }\\---------------\)
7. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-3}{4} . (\frac{-4}{3}) }= a^{1}\\\\---------------\)
8. \(\left(a^{\frac{-1}{6}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{6} . (\frac{-1}{2}) }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
9. \(\left(a^{\frac{-3}{5}}\right)^{\frac{5}{6}}\\= a^{ \frac{-3}{5} . \frac{5}{6} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
10. \(\left(x^{\frac{-3}{2}}\right)^{\frac{5}{2}}\\= x^{ \frac{-3}{2} . \frac{5}{2} }= x^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ x^{15} }}\\=\frac{1}{|x^{3}|.\sqrt[4]{ x^{3} }}=\frac{1}{|x^{3}|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{4}|}\\---------------\)
11. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{2}}\\= q^{ \frac{1}{2} . (\frac{-5}{2}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
12. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-3}{5}}\\= x^{ \frac{-3}{4} . (\frac{-3}{5}) }= x^{\frac{9}{20}}\\=\sqrt[20]{ x^{9} }\\---------------\)