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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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