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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-1}{3} . (\frac{-2}{3}) }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
2. \(\left(q^{\frac{-1}{5}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{5} . \frac{1}{2} }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
3. \(\left(y^{\frac{4}{5}}\right)^{\frac{-1}{4}}\\= y^{ \frac{4}{5} . (\frac{-1}{4}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
4. \(\left(x^{\frac{5}{3}}\right)^{1}\\= x^{ \frac{5}{3} . 1 }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
5. \(\left(x^{1}\right)^{\frac{5}{4}}\\= x^{ 1 . \frac{5}{4} }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
6. \(\left(x^{\frac{3}{5}}\right)^{1}\\= x^{ \frac{3}{5} . 1 }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
7. \(\left(q^{\frac{1}{2}}\right)^{1}\\= q^{ \frac{1}{2} . 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
8. \(\left(y^{2}\right)^{-1}\\= y^{ 2 . (-1) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
9. \(\left(y^{\frac{3}{2}}\right)^{\frac{4}{5}}\\= y^{ \frac{3}{2} . \frac{4}{5} }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)
10. \(\left(x^{\frac{-3}{4}}\right)^{\frac{3}{5}}\\= x^{ \frac{-3}{4} . \frac{3}{5} }= x^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ x^{9} }}=\frac{1}{\sqrt[20]{ x^{9} }}. \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x|}\\---------------\)
11. \(\left(x^{\frac{5}{4}}\right)^{-1}\\= x^{ \frac{5}{4} . (-1) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
12. \(\left(y^{\frac{4}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{4}{5} . (\frac{-1}{2}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)