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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{3} . (\frac{-1}{2}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
2. \(\left(y^{\frac{3}{5}}\right)^{\frac{4}{5}}\\= y^{ \frac{3}{5} . \frac{4}{5} }= y^{\frac{12}{25}}\\=\sqrt[25]{ y^{12} }\\---------------\)
3. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-1}{3} . (\frac{-3}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
4. \(\left(q^{\frac{-3}{4}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-3}{4} . (\frac{-1}{2}) }= q^{\frac{3}{8}}\\=\sqrt[8]{ q^{3} }\\---------------\)
5. \(\left(x^{\frac{3}{5}}\right)^{1}\\= x^{ \frac{3}{5} . 1 }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
6. \(\left(x^{1}\right)^{\frac{1}{2}}\\= x^{ 1 . \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
7. \(\left(x^{\frac{1}{2}}\right)^{\frac{4}{5}}\\= x^{ \frac{1}{2} . \frac{4}{5} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
8. \(\left(y^{\frac{5}{2}}\right)^{\frac{5}{2}}\\= y^{ \frac{5}{2} . \frac{5}{2} }= y^{\frac{25}{4}}\\=\sqrt[4]{ y^{25} }=|y^{6}|.\sqrt[4]{ y }\\---------------\)
9. \(\left(x^{-2}\right)^{-1}\\= x^{ -2 . (-1) }= x^{2}\\\\---------------\)
10. \(\left(q^{\frac{1}{4}}\right)^{\frac{5}{2}}\\= q^{ \frac{1}{4} . \frac{5}{2} }= q^{\frac{5}{8}}\\=\sqrt[8]{ q^{5} }\\---------------\)
11. \(\left(y^{-2}\right)^{\frac{-3}{5}}\\= y^{ -2 . (\frac{-3}{5}) }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)
12. \(\left(x^{\frac{5}{4}}\right)^{\frac{3}{4}}\\= x^{ \frac{5}{4} . \frac{3}{4} }= x^{\frac{15}{16}}\\=\sqrt[16]{ x^{15} }\\---------------\)