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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{6}}\\= y^{ \frac{1}{2} . \frac{1}{6} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
2. \(\left(q^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{1}{2} . (\frac{-2}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
3. \(\left(q^{-2}\right)^{\frac{-1}{3}}\\= q^{ -2 . (\frac{-1}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
4. \(\left(y^{\frac{4}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{4}{5} . (\frac{-1}{2}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
5. \(\left(a^{\frac{1}{5}}\right)^{1}\\= a^{ \frac{1}{5} . 1 }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
6. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{2} . (\frac{-1}{2}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
7. \(\left(a^{\frac{4}{5}}\right)^{\frac{5}{3}}\\= a^{ \frac{4}{5} . \frac{5}{3} }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
8. \(\left(a^{\frac{-1}{3}}\right)^{\frac{1}{6}}\\= a^{ \frac{-1}{3} . \frac{1}{6} }= a^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ a }}=\frac{1}{\sqrt[18]{ a }}. \color{purple}{\frac{\sqrt[18]{ a^{17} }}{\sqrt[18]{ a^{17} }}} \\=\frac{\sqrt[18]{ a^{17} }}{|a|}\\---------------\)
9. \(\left(a^{\frac{-4}{5}}\right)^{-1}\\= a^{ \frac{-4}{5} . (-1) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
10. \(\left(y^{\frac{4}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{4}{5} . \frac{1}{3} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
11. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{5}}\\= x^{ \frac{-1}{2} . \frac{1}{5} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
12. \(\left(a^{\frac{-1}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{3} . \frac{2}{3} }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)