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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{-1}\right)^{\frac{-2}{5}}\\= a^{ -1 . (\frac{-2}{5}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
2. \(\left(q^{\frac{5}{6}}\right)^{\frac{-5}{4}}\\= q^{ \frac{5}{6} . (\frac{-5}{4}) }= q^{\frac{-25}{24}}\\=\frac{1}{\sqrt[24]{ q^{25} }}\\=\frac{1}{|q|.\sqrt[24]{ q }}=\frac{1}{|q|.\sqrt[24]{ q }} \color{purple}{\frac{\sqrt[24]{ q^{23} }}{\sqrt[24]{ q^{23} }}} \\=\frac{\sqrt[24]{ q^{23} }}{|q^{2}|}\\---------------\)
3. \(\left(a^{\frac{-1}{2}}\right)^{1}\\= a^{ \frac{-1}{2} . 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
4. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-1}{4} . (\frac{-2}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
5. \(\left(a^{\frac{-3}{5}}\right)^{1}\\= a^{ \frac{-3}{5} . 1 }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
6. \(\left(a^{\frac{-4}{3}}\right)^{\frac{3}{2}}\\= a^{ \frac{-4}{3} . \frac{3}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
7. \(\left(q^{\frac{-1}{2}}\right)^{\frac{4}{3}}\\= q^{ \frac{-1}{2} . \frac{4}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
8. \(\left(x^{\frac{-5}{6}}\right)^{-2}\\= x^{ \frac{-5}{6} . (-2) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
9. \(\left(y^{-1}\right)^{\frac{-1}{2}}\\= y^{ -1 . (\frac{-1}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
10. \(\left(x^{1}\right)^{\frac{1}{2}}\\= x^{ 1 . \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
11. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{-1}{3} . \frac{1}{4} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
12. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-1}{2} . (\frac{-1}{6}) }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)