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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{5}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{5} . \frac{1}{2} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
2. \(\left(q^{\frac{1}{4}}\right)^{\frac{5}{3}}\\= q^{ \frac{1}{4} . \frac{5}{3} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
3. \(\left(x^{\frac{-1}{4}}\right)^{-1}\\= x^{ \frac{-1}{4} . (-1) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
4. \(\left(y^{\frac{-3}{2}}\right)^{\frac{5}{6}}\\= y^{ \frac{-3}{2} . \frac{5}{6} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
5. \(\left(y^{\frac{-1}{3}}\right)^{2}\\= y^{ \frac{-1}{3} . 2 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
6. \(\left(y^{\frac{3}{4}}\right)^{\frac{-1}{5}}\\= y^{ \frac{3}{4} . (\frac{-1}{5}) }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
7. \(\left(q^{\frac{1}{2}}\right)^{\frac{4}{5}}\\= q^{ \frac{1}{2} . \frac{4}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
8. \(\left(y^{\frac{-3}{2}}\right)^{\frac{3}{2}}\\= y^{ \frac{-3}{2} . \frac{3}{2} }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
9. \(\left(y^{\frac{-3}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-3}{2} . (\frac{-1}{3}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
10. \(\left(x^{\frac{5}{4}}\right)^{\frac{-1}{3}}\\= x^{ \frac{5}{4} . (\frac{-1}{3}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
11. \(\left(q^{-1}\right)^{1}\\= q^{ -1 . 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)
12. \(\left(y^{\frac{1}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{1}{5} . \frac{1}{3} }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)