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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{3}}\right)^{\frac{-4}{5}}\\= x^{ \frac{1}{3} . (\frac{-4}{5}) }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
2. \(\left(q^{\frac{2}{3}}\right)^{\frac{1}{3}}\\= q^{ \frac{2}{3} . \frac{1}{3} }= q^{\frac{2}{9}}\\=\sqrt[9]{ q^{2} }\\---------------\)
3. \(\left(q^{\frac{-1}{4}}\right)^{-1}\\= q^{ \frac{-1}{4} . (-1) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
4. \(\left(y^{\frac{1}{3}}\right)^{1}\\= y^{ \frac{1}{3} . 1 }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
5. \(\left(x^{\frac{4}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{4}{5} . \frac{2}{3} }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)
6. \(\left(a^{\frac{3}{2}}\right)^{\frac{1}{3}}\\= a^{ \frac{3}{2} . \frac{1}{3} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
7. \(\left(a^{-1}\right)^{\frac{4}{3}}\\= a^{ -1 . \frac{4}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
8. \(\left(y^{\frac{-2}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{-2}{5} . \frac{1}{3} }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
9. \(\left(y^{\frac{1}{6}}\right)^{-1}\\= y^{ \frac{1}{6} . (-1) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
10. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-1}{6} . (\frac{-1}{4}) }= q^{\frac{1}{24}}\\=\sqrt[24]{ q }\\---------------\)
11. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-4}{3} . (\frac{-5}{4}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
12. \(\left(q^{\frac{4}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{4}{3} . \frac{1}{5} }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)