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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-2}{3} . \frac{1}{2} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
2. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-1}{4} . (\frac{-1}{4}) }= y^{\frac{1}{16}}\\=\sqrt[16]{ y }\\---------------\)
3. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-5}{2}}\\= x^{ \frac{-1}{2} . (\frac{-5}{2}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
4. \(\left(y^{\frac{1}{3}}\right)^{1}\\= y^{ \frac{1}{3} . 1 }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
5. \(\left(x^{\frac{-3}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{-3}{4} . \frac{1}{2} }= x^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ x^{3} }}=\frac{1}{\sqrt[8]{ x^{3} }}. \color{purple}{\frac{\sqrt[8]{ x^{5} }}{\sqrt[8]{ x^{5} }}} \\=\frac{\sqrt[8]{ x^{5} }}{|x|}\\---------------\)
6. \(\left(y^{1}\right)^{\frac{-3}{2}}\\= y^{ 1 . (\frac{-3}{2}) }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
7. \(\left(q^{1}\right)^{\frac{3}{4}}\\= q^{ 1 . \frac{3}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
8. \(\left(q^{\frac{-5}{6}}\right)^{\frac{1}{5}}\\= q^{ \frac{-5}{6} . \frac{1}{5} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
9. \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
10. \(\left(a^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= a^{ \frac{-5}{6} . \frac{1}{2} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
11. \(\left(y^{\frac{1}{4}}\right)^{\frac{3}{5}}\\= y^{ \frac{1}{4} . \frac{3}{5} }= y^{\frac{3}{20}}\\=\sqrt[20]{ y^{3} }\\---------------\)
12. \(\left(x^{\frac{4}{5}}\right)^{\frac{1}{6}}\\= x^{ \frac{4}{5} . \frac{1}{6} }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)