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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{3}}\right)^{2}\\= a^{ \frac{-1}{3} . 2 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
2. \(\left(x^{\frac{5}{3}}\right)^{\frac{-3}{2}}\\= x^{ \frac{5}{3} . (\frac{-3}{2}) }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
3. \(\left(x^{\frac{-3}{2}}\right)^{\frac{1}{6}}\\= x^{ \frac{-3}{2} . \frac{1}{6} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
4. \(\left(x^{\frac{2}{3}}\right)^{\frac{1}{5}}\\= x^{ \frac{2}{3} . \frac{1}{5} }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)
5. \(\left(q^{\frac{-1}{3}}\right)^{-1}\\= q^{ \frac{-1}{3} . (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
6. \(\left(y^{\frac{-1}{4}}\right)^{\frac{3}{4}}\\= y^{ \frac{-1}{4} . \frac{3}{4} }= y^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ y^{3} }}=\frac{1}{\sqrt[16]{ y^{3} }}. \color{purple}{\frac{\sqrt[16]{ y^{13} }}{\sqrt[16]{ y^{13} }}} \\=\frac{\sqrt[16]{ y^{13} }}{|y|}\\---------------\)
7. \(\left(y^{\frac{3}{2}}\right)^{\frac{-4}{3}}\\= y^{ \frac{3}{2} . (\frac{-4}{3}) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
8. \(\left(x^{1}\right)^{\frac{-5}{2}}\\= x^{ 1 . (\frac{-5}{2}) }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
9. \(\left(a^{\frac{-5}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-5}{3} . \frac{1}{3} }= a^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ a^{5} }}=\frac{1}{\sqrt[9]{ a^{5} }}. \color{purple}{\frac{\sqrt[9]{ a^{4} }}{\sqrt[9]{ a^{4} }}} \\=\frac{\sqrt[9]{ a^{4} }}{a}\\---------------\)
10. \(\left(y^{\frac{-1}{2}}\right)^{1}\\= y^{ \frac{-1}{2} . 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
11. \(\left(q^{\frac{-5}{2}}\right)^{-1}\\= q^{ \frac{-5}{2} . (-1) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
12. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-4}{3} . (\frac{-1}{2}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)