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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{3}}\right)^{\frac{1}{3}}\\= q^{ \frac{-5}{3} . \frac{1}{3} }= q^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ q^{5} }}=\frac{1}{\sqrt[9]{ q^{5} }}. \color{purple}{\frac{\sqrt[9]{ q^{4} }}{\sqrt[9]{ q^{4} }}} \\=\frac{\sqrt[9]{ q^{4} }}{q}\\---------------\)
2. \(\left(a^{-1}\right)^{\frac{-2}{5}}\\= a^{ -1 . (\frac{-2}{5}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
3. \(\left(x^{\frac{-2}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{-2}{5} . \frac{1}{2} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
4. \(\left(a^{2}\right)^{1}\\= a^{ 2 . 1 }= a^{2}\\\\---------------\)
5. \(\left(x^{\frac{3}{5}}\right)^{\frac{3}{2}}\\= x^{ \frac{3}{5} . \frac{3}{2} }= x^{\frac{9}{10}}\\=\sqrt[10]{ x^{9} }\\---------------\)
6. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-4}{3} . (\frac{-4}{5}) }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
7. \(\left(y^{\frac{1}{6}}\right)^{\frac{1}{3}}\\= y^{ \frac{1}{6} . \frac{1}{3} }= y^{\frac{1}{18}}\\=\sqrt[18]{ y }\\---------------\)
8. \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{-2}{3} . \frac{1}{5} }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
9. \(\left(y^{\frac{5}{3}}\right)^{\frac{-3}{4}}\\= y^{ \frac{5}{3} . (\frac{-3}{4}) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
10. \(\left(q^{-1}\right)^{\frac{-2}{3}}\\= q^{ -1 . (\frac{-2}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
11. \(\left(x^{\frac{1}{2}}\right)^{\frac{3}{5}}\\= x^{ \frac{1}{2} . \frac{3}{5} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
12. \(\left(y^{\frac{5}{2}}\right)^{\frac{-5}{2}}\\= y^{ \frac{5}{2} . (\frac{-5}{2}) }= y^{\frac{-25}{4}}\\=\frac{1}{\sqrt[4]{ y^{25} }}\\=\frac{1}{|y^{6}|.\sqrt[4]{ y }}=\frac{1}{|y^{6}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{7}|}\\---------------\)