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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{-1}\right)^{\frac{2}{5}}\\= x^{ -1 . \frac{2}{5} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
2. \(\left(q^{\frac{2}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{2}{3} . \frac{1}{2} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
3. \(\left(a^{\frac{1}{2}}\right)^{\frac{5}{2}}\\= a^{ \frac{1}{2} . \frac{5}{2} }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
4. \(\left(a^{\frac{1}{2}}\right)^{2}\\= a^{ \frac{1}{2} . 2 }= a^{1}\\\\---------------\)
5. \(\left(a^{-1}\right)^{\frac{-1}{6}}\\= a^{ -1 . (\frac{-1}{6}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
6. \(\left(a^{\frac{3}{4}}\right)^{\frac{-3}{4}}\\= a^{ \frac{3}{4} . (\frac{-3}{4}) }= a^{\frac{-9}{16}}\\=\frac{1}{\sqrt[16]{ a^{9} }}=\frac{1}{\sqrt[16]{ a^{9} }}. \color{purple}{\frac{\sqrt[16]{ a^{7} }}{\sqrt[16]{ a^{7} }}} \\=\frac{\sqrt[16]{ a^{7} }}{|a|}\\---------------\)
7. \(\left(x^{1}\right)^{\frac{5}{2}}\\= x^{ 1 . \frac{5}{2} }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
8. \(\left(x^{1}\right)^{\frac{5}{4}}\\= x^{ 1 . \frac{5}{4} }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
9. \(\left(a^{2}\right)^{\frac{-1}{5}}\\= a^{ 2 . (\frac{-1}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
10. \(\left(x^{\frac{5}{4}}\right)^{\frac{-2}{3}}\\= x^{ \frac{5}{4} . (\frac{-2}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
11. \(\left(a^{1}\right)^{\frac{-5}{2}}\\= a^{ 1 . (\frac{-5}{2}) }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
12. \(\left(y^{\frac{-3}{4}}\right)^{\frac{2}{3}}\\= y^{ \frac{-3}{4} . \frac{2}{3} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)