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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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