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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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