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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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