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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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