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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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