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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-1}{5}}\\= a^{ \frac{-4}{5} . (\frac{-1}{5}) }= a^{\frac{4}{25}}\\=\sqrt[25]{ a^{4} }\\---------------\)
2. \(\left(a^{\frac{4}{5}}\right)^{\frac{4}{5}}\\= a^{ \frac{4}{5} . \frac{4}{5} }= a^{\frac{16}{25}}\\=\sqrt[25]{ a^{16} }\\---------------\)
3. \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{3}}\\= a^{ \frac{1}{6} . \frac{1}{3} }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
4. \(\left(q^{\frac{2}{3}}\right)^{-1}\\= q^{ \frac{2}{3} . (-1) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
5. \(\left(a^{\frac{-5}{6}}\right)^{-2}\\= a^{ \frac{-5}{6} . (-2) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
6. \(\left(q^{1}\right)^{\frac{-1}{4}}\\= q^{ 1 . (\frac{-1}{4}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
7. \(\left(q^{1}\right)^{\frac{-5}{2}}\\= q^{ 1 . (\frac{-5}{2}) }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
8. \(\left(a^{1}\right)^{\frac{2}{3}}\\= a^{ 1 . \frac{2}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
9. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-5}{4} . (\frac{-2}{5}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(\left(q^{\frac{-4}{5}}\right)^{\frac{3}{2}}\\= q^{ \frac{-4}{5} . \frac{3}{2} }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
11. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-2}{5} . (\frac{-2}{3}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
12. \(\left(a^{\frac{-1}{2}}\right)^{\frac{5}{6}}\\= a^{ \frac{-1}{2} . \frac{5}{6} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)