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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{5}}\right)^{1}\\= a^{ \frac{-1}{5} . 1 }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
2. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-2}{3} . (\frac{-1}{5}) }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)
3. \(\left(x^{\frac{-3}{2}}\right)^{1}\\= x^{ \frac{-3}{2} . 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
4. \(\left(a^{\frac{-5}{4}}\right)^{2}\\= a^{ \frac{-5}{4} . 2 }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
5. \(\left(x^{1}\right)^{1}\\= x^{ 1 . 1 }= x^{1}\\\\---------------\)
6. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-1}{3} . (\frac{-1}{6}) }= q^{\frac{1}{18}}\\=\sqrt[18]{ q }\\---------------\)
7. \(\left(q^{\frac{-3}{5}}\right)^{1}\\= q^{ \frac{-3}{5} . 1 }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
8. \(\left(a^{\frac{1}{3}}\right)^{\frac{3}{5}}\\= a^{ \frac{1}{3} . \frac{3}{5} }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
9. \(\left(x^{\frac{-2}{3}}\right)^{1}\\= x^{ \frac{-2}{3} . 1 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
10. \(\left(y^{-1}\right)^{-1}\\= y^{ -1 . (-1) }= y^{1}\\\\---------------\)
11. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{-2}{3} . \frac{1}{3} }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
12. \(\left(q^{\frac{-4}{5}}\right)^{\frac{5}{6}}\\= q^{ \frac{-4}{5} . \frac{5}{6} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)