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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{-1}\right)^{\frac{-1}{5}}\\= a^{ -1 . (\frac{-1}{5}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
2. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-3}{4}}\\= x^{ \frac{-1}{2} . (\frac{-3}{4}) }= x^{\frac{3}{8}}\\=\sqrt[8]{ x^{3} }\\---------------\)
3. \(\left(x^{\frac{1}{6}}\right)^{\frac{-5}{6}}\\= x^{ \frac{1}{6} . (\frac{-5}{6}) }= x^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ x^{5} }}=\frac{1}{\sqrt[36]{ x^{5} }}. \color{purple}{\frac{\sqrt[36]{ x^{31} }}{\sqrt[36]{ x^{31} }}} \\=\frac{\sqrt[36]{ x^{31} }}{|x|}\\---------------\)
4. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-1}{2} . (\frac{-2}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
5. \(\left(q^{-2}\right)^{1}\\= q^{ -2 . 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
6. \(\left(x^{\frac{4}{3}}\right)^{\frac{-3}{2}}\\= x^{ \frac{4}{3} . (\frac{-3}{2}) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
7. \(\left(a^{\frac{-3}{5}}\right)^{\frac{4}{5}}\\= a^{ \frac{-3}{5} . \frac{4}{5} }= a^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ a^{12} }}=\frac{1}{\sqrt[25]{ a^{12} }}. \color{purple}{\frac{\sqrt[25]{ a^{13} }}{\sqrt[25]{ a^{13} }}} \\=\frac{\sqrt[25]{ a^{13} }}{a}\\---------------\)
8. \(\left(a^{\frac{1}{4}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{4} . (\frac{-1}{2}) }= a^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ a }}=\frac{1}{\sqrt[8]{ a }}. \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a|}\\---------------\)
9. \(\left(x^{\frac{2}{3}}\right)^{\frac{5}{2}}\\= x^{ \frac{2}{3} . \frac{5}{2} }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
10. \(\left(x^{\frac{1}{2}}\right)^{\frac{2}{5}}\\= x^{ \frac{1}{2} . \frac{2}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
11. \(\left(x^{\frac{-2}{3}}\right)^{1}\\= x^{ \frac{-2}{3} . 1 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
12. \(\left(x^{\frac{2}{5}}\right)^{\frac{-5}{4}}\\= x^{ \frac{2}{5} . (\frac{-5}{4}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)