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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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