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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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