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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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