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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{-1}\right)^{\frac{2}{3}}\\= x^{ -1 . \frac{2}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
2. \(\left(a^{\frac{-1}{3}}\right)^{-1}\\= a^{ \frac{-1}{3} . (-1) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
3. \(\left(q^{-2}\right)^{\frac{3}{4}}\\= q^{ -2 . \frac{3}{4} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
4. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-3}{4}}\\= x^{ \frac{-1}{3} . (\frac{-3}{4}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
5. \(\left(x^{\frac{1}{2}}\right)^{1}\\= x^{ \frac{1}{2} . 1 }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
6. \(\left(x^{\frac{-1}{6}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-1}{6} . (\frac{-2}{3}) }= x^{\frac{1}{9}}\\=\sqrt[9]{ x }\\---------------\)
7. \(\left(q^{\frac{5}{4}}\right)^{\frac{-3}{4}}\\= q^{ \frac{5}{4} . (\frac{-3}{4}) }= q^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ q^{15} }}=\frac{1}{\sqrt[16]{ q^{15} }}. \color{purple}{\frac{\sqrt[16]{ q }}{\sqrt[16]{ q }}} \\=\frac{\sqrt[16]{ q }}{|q|}\\---------------\)
8. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-5}{3}}\\= a^{ \frac{-4}{3} . (\frac{-5}{3}) }= a^{\frac{20}{9}}\\=\sqrt[9]{ a^{20} }=a^{2}.\sqrt[9]{ a^{2} }\\---------------\)
9. \(\left(x^{\frac{3}{5}}\right)^{\frac{1}{5}}\\= x^{ \frac{3}{5} . \frac{1}{5} }= x^{\frac{3}{25}}\\=\sqrt[25]{ x^{3} }\\---------------\)
10. \(\left(q^{-1}\right)^{-1}\\= q^{ -1 . (-1) }= q^{1}\\\\---------------\)
11. \(\left(a^{\frac{1}{2}}\right)^{\frac{-4}{3}}\\= a^{ \frac{1}{2} . (\frac{-4}{3}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
12. \(\left(a^{\frac{3}{5}}\right)^{\frac{-4}{5}}\\= a^{ \frac{3}{5} . (\frac{-4}{5}) }= a^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ a^{12} }}=\frac{1}{\sqrt[25]{ a^{12} }}. \color{purple}{\frac{\sqrt[25]{ a^{13} }}{\sqrt[25]{ a^{13} }}} \\=\frac{\sqrt[25]{ a^{13} }}{a}\\---------------\)