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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-3}{2}}\right)^{\frac{1}{4}}\\= x^{ \frac{-3}{2} . \frac{1}{4} }= x^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ x^{3} }}=\frac{1}{\sqrt[8]{ x^{3} }}. \color{purple}{\frac{\sqrt[8]{ x^{5} }}{\sqrt[8]{ x^{5} }}} \\=\frac{\sqrt[8]{ x^{5} }}{|x|}\\---------------\)
2. \(\left(y^{\frac{1}{5}}\right)^{\frac{-2}{5}}\\= y^{ \frac{1}{5} . (\frac{-2}{5}) }= y^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ y^{2} }}=\frac{1}{\sqrt[25]{ y^{2} }}. \color{purple}{\frac{\sqrt[25]{ y^{23} }}{\sqrt[25]{ y^{23} }}} \\=\frac{\sqrt[25]{ y^{23} }}{y}\\---------------\)
3. \(\left(a^{\frac{-5}{4}}\right)^{-1}\\= a^{ \frac{-5}{4} . (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
4. \(\left(y^{\frac{-3}{2}}\right)^{1}\\= y^{ \frac{-3}{2} . 1 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
5. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-2}{3} . (\frac{-1}{3}) }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)
6. \(\left(y^{\frac{5}{2}}\right)^{1}\\= y^{ \frac{5}{2} . 1 }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
7. \(\left(y^{\frac{-2}{3}}\right)^{\frac{5}{3}}\\= y^{ \frac{-2}{3} . \frac{5}{3} }= y^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ y^{10} }}\\=\frac{1}{y.\sqrt[9]{ y }}=\frac{1}{y.\sqrt[9]{ y }} \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y^{2}}\\---------------\)
8. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-3}{4} . (\frac{-4}{5}) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
9. \(\left(x^{-1}\right)^{\frac{-2}{3}}\\= x^{ -1 . (\frac{-2}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
10. \(\left(y^{-1}\right)^{1}\\= y^{ -1 . 1 }= y^{-1}\\=\frac{1}{y}\\---------------\)
11. \(\left(x^{\frac{2}{3}}\right)^{\frac{-1}{4}}\\= x^{ \frac{2}{3} . (\frac{-1}{4}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
12. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{3} . \frac{1}{3} }= q^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ q }}=\frac{1}{\sqrt[9]{ q }}. \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q}\\---------------\)