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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-3}{2}}\right)^{-1}\\= q^{ \frac{-3}{2} . (-1) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
2. \(\left(y^{\frac{2}{3}}\right)^{\frac{3}{2}}\\= y^{ \frac{2}{3} . \frac{3}{2} }= y^{1}\\\\---------------\)
3. \(\left(a^{\frac{2}{5}}\right)^{\frac{-1}{3}}\\= a^{ \frac{2}{5} . (\frac{-1}{3}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
4. \(\left(a^{\frac{-3}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{-3}{5} . \frac{1}{3} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
5. \(\left(x^{\frac{-4}{3}}\right)^{1}\\= x^{ \frac{-4}{3} . 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
6. \(\left(x^{\frac{-2}{3}}\right)^{-1}\\= x^{ \frac{-2}{3} . (-1) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{-1}{2}}\\= a^{ -1 . (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
8. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-1}{2} . (\frac{-5}{6}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
9. \(\left(a^{\frac{2}{3}}\right)^{\frac{-3}{5}}\\= a^{ \frac{2}{3} . (\frac{-3}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
10. \(\left(a^{\frac{5}{6}}\right)^{\frac{-1}{6}}\\= a^{ \frac{5}{6} . (\frac{-1}{6}) }= a^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ a^{5} }}=\frac{1}{\sqrt[36]{ a^{5} }}. \color{purple}{\frac{\sqrt[36]{ a^{31} }}{\sqrt[36]{ a^{31} }}} \\=\frac{\sqrt[36]{ a^{31} }}{|a|}\\---------------\)
11. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
12. \(\left(y^{1}\right)^{\frac{3}{4}}\\= y^{ 1 . \frac{3}{4} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)