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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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