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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-5}{3}}\right)^{\frac{3}{4}}\\= a^{ \frac{-5}{3} . \frac{3}{4} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
2. \(\left(a^{\frac{1}{4}}\right)^{1}\\= a^{ \frac{1}{4} . 1 }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
3. \(\left(a^{1}\right)^{\frac{-2}{3}}\\= a^{ 1 . (\frac{-2}{3}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
4. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-2}{3} . (\frac{-5}{6}) }= y^{\frac{5}{9}}\\=\sqrt[9]{ y^{5} }\\---------------\)
5. \(\left(q^{\frac{1}{6}}\right)^{\frac{-3}{5}}\\= q^{ \frac{1}{6} . (\frac{-3}{5}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
6. \(\left(x^{\frac{-1}{6}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{6} . \frac{1}{2} }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
7. \(\left(a^{\frac{-3}{4}}\right)^{\frac{5}{3}}\\= a^{ \frac{-3}{4} . \frac{5}{3} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
8. \(\left(q^{\frac{5}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{5}{2} . \frac{2}{3} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
9. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-2}{5} . (\frac{-1}{5}) }= q^{\frac{2}{25}}\\=\sqrt[25]{ q^{2} }\\---------------\)
10. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{1}{2} . \frac{1}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
11. \(\left(q^{\frac{3}{2}}\right)^{1}\\= q^{ \frac{3}{2} . 1 }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
12. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-1}{6} . (\frac{-5}{4}) }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)