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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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