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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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