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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{-2}\right)^{1}\\= x^{ -2 . 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
2. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{2} . (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
3. \(\left(y^{-1}\right)^{\frac{-1}{4}}\\= y^{ -1 . (\frac{-1}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
4. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-2}{3} . (\frac{-1}{3}) }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
5. \(\left(a^{\frac{-1}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{4} . \frac{1}{2} }= a^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ a }}=\frac{1}{\sqrt[8]{ a }}. \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a|}\\---------------\)
6. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-1}{2} . (\frac{-3}{2}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
7. \(\left(y^{\frac{3}{5}}\right)^{\frac{5}{6}}\\= y^{ \frac{3}{5} . \frac{5}{6} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
8. \(\left(y^{\frac{-5}{6}}\right)^{\frac{5}{6}}\\= y^{ \frac{-5}{6} . \frac{5}{6} }= y^{\frac{-25}{36}}\\=\frac{1}{\sqrt[36]{ y^{25} }}=\frac{1}{\sqrt[36]{ y^{25} }}. \color{purple}{\frac{\sqrt[36]{ y^{11} }}{\sqrt[36]{ y^{11} }}} \\=\frac{\sqrt[36]{ y^{11} }}{|y|}\\---------------\)
9. \(\left(q^{\frac{3}{4}}\right)^{\frac{4}{5}}\\= q^{ \frac{3}{4} . \frac{4}{5} }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
10. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{4} . (\frac{-1}{2}) }= q^{\frac{1}{8}}\\=\sqrt[8]{ q }\\---------------\)
11. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-1}{3} . (\frac{-5}{4}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
12. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-2}{5} . (\frac{-3}{4}) }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)