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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{-1}\right)^{\frac{-1}{2}}\\= y^{ -1 . (\frac{-1}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
2. \(\left(a^{-1}\right)^{\frac{1}{5}}\\= a^{ -1 . \frac{1}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
3. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-1}{3} . (\frac{-2}{3}) }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
4. \(\left(a^{2}\right)^{\frac{-5}{6}}\\= a^{ 2 . (\frac{-5}{6}) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
5. \(\left(x^{-1}\right)^{\frac{-2}{3}}\\= x^{ -1 . (\frac{-2}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
6. \(\left(x^{1}\right)^{\frac{-1}{6}}\\= x^{ 1 . (\frac{-1}{6}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
7. \(\left(q^{\frac{-3}{4}}\right)^{1}\\= q^{ \frac{-3}{4} . 1 }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
8. \(\left(a^{-1}\right)^{\frac{-3}{5}}\\= a^{ -1 . (\frac{-3}{5}) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
9. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-3}{2}}\\= y^{ \frac{-2}{5} . (\frac{-3}{2}) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
10. \(\left(q^{\frac{1}{3}}\right)^{\frac{1}{6}}\\= q^{ \frac{1}{3} . \frac{1}{6} }= q^{\frac{1}{18}}\\=\sqrt[18]{ q }\\---------------\)
11. \(\left(x^{\frac{1}{4}}\right)^{\frac{-3}{5}}\\= x^{ \frac{1}{4} . (\frac{-3}{5}) }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)
12. \(\left(y^{-1}\right)^{\frac{2}{3}}\\= y^{ -1 . \frac{2}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)