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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-4}{3}}\\= x^{ \frac{-1}{3} . (\frac{-4}{3}) }= x^{\frac{4}{9}}\\=\sqrt[9]{ x^{4} }\\---------------\)
2. \(\left(a^{1}\right)^{\frac{1}{5}}\\= a^{ 1 . \frac{1}{5} }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
3. \(\left(x^{\frac{3}{5}}\right)^{\frac{-1}{3}}\\= x^{ \frac{3}{5} . (\frac{-1}{3}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
4. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-1}{2} . (\frac{-3}{4}) }= y^{\frac{3}{8}}\\=\sqrt[8]{ y^{3} }\\---------------\)
5. \(\left(a^{1}\right)^{\frac{-2}{3}}\\= a^{ 1 . (\frac{-2}{3}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
6. \(\left(q^{\frac{2}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{2}{3} . \frac{1}{5} }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
7. \(\left(a^{\frac{-1}{3}}\right)^{\frac{5}{6}}\\= a^{ \frac{-1}{3} . \frac{5}{6} }= a^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ a^{5} }}=\frac{1}{\sqrt[18]{ a^{5} }}. \color{purple}{\frac{\sqrt[18]{ a^{13} }}{\sqrt[18]{ a^{13} }}} \\=\frac{\sqrt[18]{ a^{13} }}{|a|}\\---------------\)
8. \(\left(y^{-1}\right)^{\frac{1}{5}}\\= y^{ -1 . \frac{1}{5} }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
9. \(\left(x^{-2}\right)^{\frac{1}{2}}\\= x^{ -2 . \frac{1}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
10. \(\left(x^{\frac{5}{6}}\right)^{\frac{-2}{5}}\\= x^{ \frac{5}{6} . (\frac{-2}{5}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
11. \(\left(a^{1}\right)^{\frac{-3}{2}}\\= a^{ 1 . (\frac{-3}{2}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
12. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{2}}\\= q^{ \frac{1}{2} . (\frac{-5}{2}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)