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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{5}}\right)^{1}\\= a^{ \frac{-1}{5} . 1 }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
2. \(\left(x^{\frac{-5}{2}}\right)^{\frac{1}{3}}\\= x^{ \frac{-5}{2} . \frac{1}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
3. \(\left(a^{\frac{1}{2}}\right)^{\frac{-2}{5}}\\= a^{ \frac{1}{2} . (\frac{-2}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
4. \(\left(x^{\frac{1}{6}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{6} . (\frac{-2}{3}) }= x^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ x }}=\frac{1}{\sqrt[9]{ x }}. \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x}\\---------------\)
5. \(\left(a^{\frac{1}{6}}\right)^{\frac{-1}{6}}\\= a^{ \frac{1}{6} . (\frac{-1}{6}) }= a^{\frac{-1}{36}}\\=\frac{1}{\sqrt[36]{ a }}=\frac{1}{\sqrt[36]{ a }}. \color{purple}{\frac{\sqrt[36]{ a^{35} }}{\sqrt[36]{ a^{35} }}} \\=\frac{\sqrt[36]{ a^{35} }}{|a|}\\---------------\)
6. \(\left(q^{\frac{-2}{3}}\right)^{-1}\\= q^{ \frac{-2}{3} . (-1) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
7. \(\left(q^{\frac{-1}{2}}\right)^{\frac{3}{5}}\\= q^{ \frac{-1}{2} . \frac{3}{5} }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
8. \(\left(x^{2}\right)^{2}\\= x^{ 2 . 2 }= x^{4}\\\\---------------\)
9. \(\left(y^{\frac{3}{4}}\right)^{\frac{1}{5}}\\= y^{ \frac{3}{4} . \frac{1}{5} }= y^{\frac{3}{20}}\\=\sqrt[20]{ y^{3} }\\---------------\)
10. \(\left(y^{\frac{-4}{5}}\right)^{\frac{1}{2}}\\= y^{ \frac{-4}{5} . \frac{1}{2} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
11. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-2}{5} . (\frac{-1}{4}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
12. \(\left(a^{1}\right)^{\frac{-3}{2}}\\= a^{ 1 . (\frac{-3}{2}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)