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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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