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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-2}{3} . (\frac{-3}{2}) }= x^{1}\\\\---------------\)
2. \(\left(a^{\frac{2}{5}}\right)^{\frac{-4}{3}}\\= a^{ \frac{2}{5} . (\frac{-4}{3}) }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
3. \(\left(q^{\frac{1}{2}}\right)^{2}\\= q^{ \frac{1}{2} . 2 }= q^{1}\\\\---------------\)
4. \(\left(q^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{3} . (\frac{-1}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
5. \(\left(a^{\frac{1}{3}}\right)^{\frac{-5}{3}}\\= a^{ \frac{1}{3} . (\frac{-5}{3}) }= a^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ a^{5} }}=\frac{1}{\sqrt[9]{ a^{5} }}. \color{purple}{\frac{\sqrt[9]{ a^{4} }}{\sqrt[9]{ a^{4} }}} \\=\frac{\sqrt[9]{ a^{4} }}{a}\\---------------\)
6. \(\left(a^{\frac{-1}{4}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{4} . \frac{2}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
7. \(\left(q^{\frac{1}{3}}\right)^{\frac{4}{3}}\\= q^{ \frac{1}{3} . \frac{4}{3} }= q^{\frac{4}{9}}\\=\sqrt[9]{ q^{4} }\\---------------\)
8. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-2}{5}}\\= y^{ \frac{-1}{2} . (\frac{-2}{5}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
9. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-1}{3} . (\frac{-1}{5}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
10. \(\left(a^{\frac{4}{5}}\right)^{\frac{-4}{3}}\\= a^{ \frac{4}{5} . (\frac{-4}{3}) }= a^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ a^{16} }}\\=\frac{1}{a.\sqrt[15]{ a }}=\frac{1}{a.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{2}}\\---------------\)
11. \(\left(y^{-1}\right)^{-2}\\= y^{ -1 . (-2) }= y^{2}\\\\---------------\)
12. \(\left(a^{\frac{4}{5}}\right)^{\frac{1}{5}}\\= a^{ \frac{4}{5} . \frac{1}{5} }= a^{\frac{4}{25}}\\=\sqrt[25]{ a^{4} }\\---------------\)