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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{4}{5}}\\= q^{ 1 . \frac{4}{5} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
2. \(\left(y^{\frac{-1}{2}}\right)^{1}\\= y^{ \frac{-1}{2} . 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\left(x^{\frac{3}{2}}\right)^{\frac{-5}{3}}\\= x^{ \frac{3}{2} . (\frac{-5}{3}) }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
4. \(\left(x^{\frac{4}{3}}\right)^{\frac{-3}{2}}\\= x^{ \frac{4}{3} . (\frac{-3}{2}) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
5. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-5}{3}}\\= x^{ \frac{-5}{6} . (\frac{-5}{3}) }= x^{\frac{25}{18}}\\=\sqrt[18]{ x^{25} }=|x|.\sqrt[18]{ x^{7} }\\---------------\)
6. \(\left(q^{\frac{3}{2}}\right)^{\frac{5}{2}}\\= q^{ \frac{3}{2} . \frac{5}{2} }= q^{\frac{15}{4}}\\=\sqrt[4]{ q^{15} }=|q^{3}|.\sqrt[4]{ q^{3} }\\---------------\)
7. \(\left(y^{\frac{5}{3}}\right)^{\frac{2}{5}}\\= y^{ \frac{5}{3} . \frac{2}{5} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
8. \(\left(q^{\frac{-1}{3}}\right)^{\frac{5}{2}}\\= q^{ \frac{-1}{3} . \frac{5}{2} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
9. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-5}{3} . (\frac{-2}{3}) }= a^{\frac{10}{9}}\\=\sqrt[9]{ a^{10} }=a.\sqrt[9]{ a }\\---------------\)
10. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-2}{5} . (\frac{-3}{2}) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
11. \(\left(y^{\frac{1}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{1}{3} . \frac{1}{3} }= y^{\frac{1}{9}}\\=\sqrt[9]{ y }\\---------------\)
12. \(\left(a^{\frac{3}{5}}\right)^{\frac{4}{3}}\\= a^{ \frac{3}{5} . \frac{4}{3} }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)