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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-2}{3} . (\frac{-1}{4}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
2. \(\left(q^{\frac{3}{2}}\right)^{\frac{5}{4}}\\= q^{ \frac{3}{2} . \frac{5}{4} }= q^{\frac{15}{8}}\\=\sqrt[8]{ q^{15} }=|q|.\sqrt[8]{ q^{7} }\\---------------\)
3. \(\left(q^{\frac{-1}{5}}\right)^{\frac{5}{3}}\\= q^{ \frac{-1}{5} . \frac{5}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
4. \(\left(q^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{5} . (\frac{-1}{2}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
5. \(\left(q^{\frac{1}{3}}\right)^{\frac{-2}{3}}\\= q^{ \frac{1}{3} . (\frac{-2}{3}) }= q^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ q^{2} }}=\frac{1}{\sqrt[9]{ q^{2} }}. \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q}\\---------------\)
6. \(\left(y^{\frac{-3}{4}}\right)^{1}\\= y^{ \frac{-3}{4} . 1 }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
7. \(\left(q^{\frac{4}{5}}\right)^{\frac{4}{3}}\\= q^{ \frac{4}{5} . \frac{4}{3} }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
8. \(\left(y^{\frac{5}{2}}\right)^{\frac{5}{4}}\\= y^{ \frac{5}{2} . \frac{5}{4} }= y^{\frac{25}{8}}\\=\sqrt[8]{ y^{25} }=|y^{3}|.\sqrt[8]{ y }\\---------------\)
9. \(\left(x^{1}\right)^{\frac{2}{3}}\\= x^{ 1 . \frac{2}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
10. \(\left(x^{\frac{1}{3}}\right)^{\frac{4}{3}}\\= x^{ \frac{1}{3} . \frac{4}{3} }= x^{\frac{4}{9}}\\=\sqrt[9]{ x^{4} }\\---------------\)
11. \(\left(y^{1}\right)^{\frac{-1}{2}}\\= y^{ 1 . (\frac{-1}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
12. \(\left(x^{\frac{1}{3}}\right)^{\frac{3}{2}}\\= x^{ \frac{1}{3} . \frac{3}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)