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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-4}{5}}\right)^{\frac{4}{5}}\\= a^{ \frac{-4}{5} . \frac{4}{5} }= a^{\frac{-16}{25}}\\=\frac{1}{\sqrt[25]{ a^{16} }}=\frac{1}{\sqrt[25]{ a^{16} }}. \color{purple}{\frac{\sqrt[25]{ a^{9} }}{\sqrt[25]{ a^{9} }}} \\=\frac{\sqrt[25]{ a^{9} }}{a}\\---------------\)
2. \(\left(x^{\frac{1}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{4} . \frac{1}{2} }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
3. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
4. \(\left(q^{\frac{5}{4}}\right)^{\frac{4}{5}}\\= q^{ \frac{5}{4} . \frac{4}{5} }= q^{1}\\\\---------------\)
5. \(\left(a^{\frac{-1}{2}}\right)^{\frac{3}{5}}\\= a^{ \frac{-1}{2} . \frac{3}{5} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
6. \(\left(a^{\frac{5}{6}}\right)^{\frac{-1}{6}}\\= a^{ \frac{5}{6} . (\frac{-1}{6}) }= a^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ a^{5} }}=\frac{1}{\sqrt[36]{ a^{5} }}. \color{purple}{\frac{\sqrt[36]{ a^{31} }}{\sqrt[36]{ a^{31} }}} \\=\frac{\sqrt[36]{ a^{31} }}{|a|}\\---------------\)
7. \(\left(x^{\frac{2}{5}}\right)^{\frac{-1}{6}}\\= x^{ \frac{2}{5} . (\frac{-1}{6}) }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
8. \(\left(q^{\frac{1}{3}}\right)^{1}\\= q^{ \frac{1}{3} . 1 }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
9. \(\left(q^{\frac{4}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{4}{3} . \frac{1}{4} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\left(x^{\frac{3}{5}}\right)^{1}\\= x^{ \frac{3}{5} . 1 }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
11. \(\left(q^{-1}\right)^{\frac{-1}{3}}\\= q^{ -1 . (\frac{-1}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
12. \(\left(a^{\frac{2}{5}}\right)^{\frac{1}{6}}\\= a^{ \frac{2}{5} . \frac{1}{6} }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)