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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{2}{3}}\right)^{\frac{-3}{4}}\\= q^{ \frac{2}{3} . (\frac{-3}{4}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
2. \(\left(q^{-1}\right)^{1}\\= q^{ -1 . 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)
3. \(\left(x^{-1}\right)^{\frac{1}{3}}\\= x^{ -1 . \frac{1}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
4. \(\left(y^{\frac{2}{3}}\right)^{\frac{3}{2}}\\= y^{ \frac{2}{3} . \frac{3}{2} }= y^{1}\\\\---------------\)
5. \(\left(a^{\frac{4}{3}}\right)^{-1}\\= a^{ \frac{4}{3} . (-1) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
6. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{2} . (\frac{-2}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
7. \(\left(x^{\frac{-1}{2}}\right)^{\frac{5}{2}}\\= x^{ \frac{-1}{2} . \frac{5}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
8. \(\left(y^{\frac{-4}{3}}\right)^{-1}\\= y^{ \frac{-4}{3} . (-1) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
9. \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{3}}\\= a^{ \frac{1}{6} . \frac{1}{3} }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
10. \(\left(x^{\frac{1}{3}}\right)^{-2}\\= x^{ \frac{1}{3} . (-2) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
11. \(\left(q^{2}\right)^{\frac{3}{2}}\\= q^{ 2 . \frac{3}{2} }= q^{3}\\\\---------------\)
12. \(\left(a^{\frac{-3}{5}}\right)^{\frac{2}{3}}\\= a^{ \frac{-3}{5} . \frac{2}{3} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)