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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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