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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{2}}\right)^{1}\\= a^{ \frac{-1}{2} . 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
2. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-2}{5} . (\frac{-1}{5}) }= q^{\frac{2}{25}}\\=\sqrt[25]{ q^{2} }\\---------------\)
3. \(\left(y^{\frac{5}{3}}\right)^{\frac{-1}{6}}\\= y^{ \frac{5}{3} . (\frac{-1}{6}) }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
4. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-5}{3} . (\frac{-2}{3}) }= a^{\frac{10}{9}}\\=\sqrt[9]{ a^{10} }=a.\sqrt[9]{ a }\\---------------\)
5. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-1}{2} . (\frac{-2}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
6. \(\left(x^{\frac{-1}{6}}\right)^{\frac{5}{6}}\\= x^{ \frac{-1}{6} . \frac{5}{6} }= x^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ x^{5} }}=\frac{1}{\sqrt[36]{ x^{5} }}. \color{purple}{\frac{\sqrt[36]{ x^{31} }}{\sqrt[36]{ x^{31} }}} \\=\frac{\sqrt[36]{ x^{31} }}{|x|}\\---------------\)
7. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{4}}\\= a^{ \frac{1}{3} . \frac{1}{4} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
8. \(\left(y^{\frac{3}{2}}\right)^{2}\\= y^{ \frac{3}{2} . 2 }= y^{3}\\\\---------------\)
9. \(\left(x^{\frac{3}{4}}\right)^{\frac{-1}{2}}\\= x^{ \frac{3}{4} . (\frac{-1}{2}) }= x^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ x^{3} }}=\frac{1}{\sqrt[8]{ x^{3} }}. \color{purple}{\frac{\sqrt[8]{ x^{5} }}{\sqrt[8]{ x^{5} }}} \\=\frac{\sqrt[8]{ x^{5} }}{|x|}\\---------------\)
10. \(\left(q^{-1}\right)^{\frac{-3}{2}}\\= q^{ -1 . (\frac{-3}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
11. \(\left(q^{\frac{-5}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{-5}{3} . \frac{1}{5} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
12. \(\left(q^{-2}\right)^{\frac{-1}{4}}\\= q^{ -2 . (\frac{-1}{4}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)