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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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