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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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