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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{6}}\right)^{\frac{-2}{5}}\\= q^{ \frac{1}{6} . (\frac{-2}{5}) }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
2. \(\left(a^{-1}\right)^{\frac{-5}{2}}\\= a^{ -1 . (\frac{-5}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
3. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{1}{2} . (\frac{-1}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
4. \(\left(a^{\frac{-1}{3}}\right)^{\frac{4}{5}}\\= a^{ \frac{-1}{3} . \frac{4}{5} }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
5. \(\left(q^{\frac{3}{4}}\right)^{\frac{2}{5}}\\= q^{ \frac{3}{4} . \frac{2}{5} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
6. \(\left(q^{-1}\right)^{\frac{-5}{4}}\\= q^{ -1 . (\frac{-5}{4}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
7. \(\left(y^{\frac{-3}{4}}\right)^{\frac{1}{3}}\\= y^{ \frac{-3}{4} . \frac{1}{3} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
8. \(\left(q^{\frac{1}{3}}\right)^{\frac{3}{2}}\\= q^{ \frac{1}{3} . \frac{3}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
9. \(\left(x^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= x^{ \frac{1}{2} . \frac{1}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
10. \(\left(q^{\frac{-2}{3}}\right)^{\frac{3}{5}}\\= q^{ \frac{-2}{3} . \frac{3}{5} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
11. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-1}{4} . (\frac{-2}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
12. \(\left(a^{\frac{-1}{2}}\right)^{\frac{4}{5}}\\= a^{ \frac{-1}{2} . \frac{4}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)