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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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