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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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