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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-3}{2}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-3}{2} . (\frac{-3}{4}) }= a^{\frac{9}{8}}\\=\sqrt[8]{ a^{9} }=|a|.\sqrt[8]{ a }\\---------------\)
2. \(\left(a^{\frac{4}{3}}\right)^{\frac{1}{4}}\\= a^{ \frac{4}{3} . \frac{1}{4} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
3. \(\left(y^{2}\right)^{\frac{1}{2}}\\= y^{ 2 . \frac{1}{2} }= y^{1}\\\\---------------\)
4. \(\left(y^{\frac{-2}{3}}\right)^{\frac{3}{5}}\\= y^{ \frac{-2}{3} . \frac{3}{5} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
5. \(\left(q^{1}\right)^{\frac{1}{3}}\\= q^{ 1 . \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
6. \(\left(y^{\frac{-3}{4}}\right)^{\frac{2}{3}}\\= y^{ \frac{-3}{4} . \frac{2}{3} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
7. \(\left(y^{\frac{5}{2}}\right)^{\frac{-5}{4}}\\= y^{ \frac{5}{2} . (\frac{-5}{4}) }= y^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ y^{25} }}\\=\frac{1}{|y^{3}|.\sqrt[8]{ y }}=\frac{1}{|y^{3}|.\sqrt[8]{ y }} \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y^{4}|}\\---------------\)
8. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{3} . (\frac{-1}{2}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
9. \(\left(x^{\frac{-3}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-3}{5} . (\frac{-1}{2}) }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
10. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{3} . \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
11. \(\left(x^{1}\right)^{1}\\= x^{ 1 . 1 }= x^{1}\\\\---------------\)
12. \(\left(a^{\frac{5}{4}}\right)^{-2}\\= a^{ \frac{5}{4} . (-2) }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)