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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{3}}\right)^{\frac{-3}{4}}\\= a^{ \frac{1}{3} . (\frac{-3}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
2. \(\left(q^{\frac{2}{3}}\right)^{\frac{-3}{5}}\\= q^{ \frac{2}{3} . (\frac{-3}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
3. \(\left(x^{\frac{-3}{5}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-3}{5} . (\frac{-1}{4}) }= x^{\frac{3}{20}}\\=\sqrt[20]{ x^{3} }\\---------------\)
4. \(\left(y^{\frac{5}{3}}\right)^{\frac{-5}{6}}\\= y^{ \frac{5}{3} . (\frac{-5}{6}) }= y^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[18]{ y^{7} }}=\frac{1}{|y|.\sqrt[18]{ y^{7} }} \color{purple}{\frac{\sqrt[18]{ y^{11} }}{\sqrt[18]{ y^{11} }}} \\=\frac{\sqrt[18]{ y^{11} }}{|y^{2}|}\\---------------\)
5. \(\left(a^{\frac{-1}{2}}\right)^{\frac{2}{5}}\\= a^{ \frac{-1}{2} . \frac{2}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
6. \(\left(a^{\frac{5}{3}}\right)^{1}\\= a^{ \frac{5}{3} . 1 }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\left(a^{\frac{-5}{3}}\right)^{\frac{3}{2}}\\= a^{ \frac{-5}{3} . \frac{3}{2} }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
8. \(\left(a^{\frac{4}{3}}\right)^{-2}\\= a^{ \frac{4}{3} . (-2) }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
9. \(\left(x^{1}\right)^{\frac{2}{3}}\\= x^{ 1 . \frac{2}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
10. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)
11. \(\left(a^{\frac{3}{5}}\right)^{\frac{5}{3}}\\= a^{ \frac{3}{5} . \frac{5}{3} }= a^{1}\\\\---------------\)
12. \(\left(x^{\frac{-5}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-5}{2} . (\frac{-2}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)