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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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