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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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