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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{-1}\right)^{\frac{3}{5}}\\= a^{ -1 . \frac{3}{5} }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
2. \(\left(x^{1}\right)^{\frac{-3}{5}}\\= x^{ 1 . (\frac{-3}{5}) }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
3. \(\left(y^{-2}\right)^{\frac{-5}{4}}\\= y^{ -2 . (\frac{-5}{4}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
4. \(\left(y^{\frac{2}{3}}\right)^{1}\\= y^{ \frac{2}{3} . 1 }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
5. \(\left(x^{2}\right)^{\frac{5}{2}}\\= x^{ 2 . \frac{5}{2} }= x^{5}\\\\---------------\)
6. \(\left(a^{\frac{1}{4}}\right)^{\frac{-1}{5}}\\= a^{ \frac{1}{4} . (\frac{-1}{5}) }= a^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ a }}=\frac{1}{\sqrt[20]{ a }}. \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a|}\\---------------\)
7. \(\left(y^{\frac{1}{4}}\right)^{\frac{1}{5}}\\= y^{ \frac{1}{4} . \frac{1}{5} }= y^{\frac{1}{20}}\\=\sqrt[20]{ y }\\---------------\)
8. \(\left(x^{\frac{1}{6}}\right)^{\frac{5}{3}}\\= x^{ \frac{1}{6} . \frac{5}{3} }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)
9. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-3}{4} . (\frac{-1}{3}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
10. \(\left(q^{\frac{-4}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-4}{5} . (\frac{-1}{2}) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
11. \(\left(x^{\frac{-2}{5}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-2}{5} . (\frac{-5}{4}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\left(y^{2}\right)^{\frac{-2}{3}}\\= y^{ 2 . (\frac{-2}{3}) }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)