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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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