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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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