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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{\frac{-1}{2}}\\= q^{ -1 . (\frac{-1}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
2. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-5}{6} . (\frac{-1}{4}) }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
3. \(\left(q^{\frac{5}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{5}{2} . \frac{1}{2} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
4. \(\left(q^{\frac{-5}{3}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-5}{3} . (\frac{-3}{2}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
5. \(\left(y^{\frac{2}{3}}\right)^{-1}\\= y^{ \frac{2}{3} . (-1) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
6. \(\left(x^{-1}\right)^{\frac{1}{3}}\\= x^{ -1 . \frac{1}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
7. \(\left(a^{\frac{1}{3}}\right)^{1}\\= a^{ \frac{1}{3} . 1 }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
8. \(\left(q^{\frac{-5}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{-5}{2} . \frac{2}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
9. \(\left(x^{\frac{-4}{5}}\right)^{-1}\\= x^{ \frac{-4}{5} . (-1) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
10. \(\left(y^{\frac{-5}{3}}\right)^{\frac{5}{6}}\\= y^{ \frac{-5}{3} . \frac{5}{6} }= y^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[18]{ y^{7} }}=\frac{1}{|y|.\sqrt[18]{ y^{7} }} \color{purple}{\frac{\sqrt[18]{ y^{11} }}{\sqrt[18]{ y^{11} }}} \\=\frac{\sqrt[18]{ y^{11} }}{|y^{2}|}\\---------------\)
11. \(\left(q^{\frac{5}{2}}\right)^{\frac{3}{5}}\\= q^{ \frac{5}{2} . \frac{3}{5} }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
12. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{2} . \frac{1}{2} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)