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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-1}{2} . (\frac{-4}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
2. \(\left(a^{\frac{5}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{5}{4} . \frac{1}{2} }= a^{\frac{5}{8}}\\=\sqrt[8]{ a^{5} }\\---------------\)
3. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
4. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{1}{2} . \frac{1}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
5. \(\left(q^{\frac{-2}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{-2}{5} . \frac{1}{3} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
6. \(\left(x^{-1}\right)^{\frac{4}{3}}\\= x^{ -1 . \frac{4}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
7. \(\left(x^{\frac{1}{5}}\right)^{\frac{-1}{3}}\\= x^{ \frac{1}{5} . (\frac{-1}{3}) }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
8. \(\left(y^{\frac{1}{3}}\right)^{\frac{4}{5}}\\= y^{ \frac{1}{3} . \frac{4}{5} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
9. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-5}{3}}\\= x^{ \frac{-1}{4} . (\frac{-5}{3}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
10. \(\left(y^{\frac{1}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{1}{3} . \frac{2}{3} }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
11. \(\left(a^{\frac{3}{2}}\right)^{\frac{2}{3}}\\= a^{ \frac{3}{2} . \frac{2}{3} }= a^{1}\\\\---------------\)
12. \(\left(a^{-2}\right)^{2}\\= a^{ -2 . 2 }= a^{-4}\\=\frac{1}{a^{4}}\\---------------\)