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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-2}\right)^{\frac{2}{3}}\\= q^{ -2 . \frac{2}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
2. \(\left(a^{\frac{4}{5}}\right)^{\frac{2}{3}}\\= a^{ \frac{4}{5} . \frac{2}{3} }= a^{\frac{8}{15}}\\=\sqrt[15]{ a^{8} }\\---------------\)
3. \(\left(a^{\frac{-3}{2}}\right)^{\frac{5}{3}}\\= a^{ \frac{-3}{2} . \frac{5}{3} }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
4. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)
5. \(\left(x^{-1}\right)^{-1}\\= x^{ -1 . (-1) }= x^{1}\\\\---------------\)
6. \(\left(x^{\frac{-4}{5}}\right)^{\frac{4}{5}}\\= x^{ \frac{-4}{5} . \frac{4}{5} }= x^{\frac{-16}{25}}\\=\frac{1}{\sqrt[25]{ x^{16} }}=\frac{1}{\sqrt[25]{ x^{16} }}. \color{purple}{\frac{\sqrt[25]{ x^{9} }}{\sqrt[25]{ x^{9} }}} \\=\frac{\sqrt[25]{ x^{9} }}{x}\\---------------\)
7. \(\left(q^{\frac{-2}{3}}\right)^{\frac{3}{5}}\\= q^{ \frac{-2}{3} . \frac{3}{5} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
8. \(\left(x^{\frac{3}{2}}\right)^{-1}\\= x^{ \frac{3}{2} . (-1) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
9. \(\left(a^{\frac{-2}{3}}\right)^{-1}\\= a^{ \frac{-2}{3} . (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
10. \(\left(x^{\frac{2}{3}}\right)^{2}\\= x^{ \frac{2}{3} . 2 }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
11. \(\left(x^{\frac{-4}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{-4}{3} . \frac{1}{3} }= x^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ x^{4} }}=\frac{1}{\sqrt[9]{ x^{4} }}. \color{purple}{\frac{\sqrt[9]{ x^{5} }}{\sqrt[9]{ x^{5} }}} \\=\frac{\sqrt[9]{ x^{5} }}{x}\\---------------\)
12. \(\left(q^{1}\right)^{\frac{5}{2}}\\= q^{ 1 . \frac{5}{2} }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)