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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{1}{3} . \frac{2}{3} }= x^{\frac{2}{9}}\\=\sqrt[9]{ x^{2} }\\---------------\)
2. \(\left(q^{\frac{1}{6}}\right)^{\frac{1}{6}}\\= q^{ \frac{1}{6} . \frac{1}{6} }= q^{\frac{1}{36}}\\=\sqrt[36]{ q }\\---------------\)
3. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-4}{3} . (\frac{-1}{6}) }= q^{\frac{2}{9}}\\=\sqrt[9]{ q^{2} }\\---------------\)
4. \(\left(q^{-1}\right)^{\frac{5}{4}}\\= q^{ -1 . \frac{5}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
5. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-2}{3} . (\frac{-1}{3}) }= q^{\frac{2}{9}}\\=\sqrt[9]{ q^{2} }\\---------------\)
6. \(\left(q^{1}\right)^{\frac{1}{6}}\\= q^{ 1 . \frac{1}{6} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
7. \(\left(a^{-1}\right)^{2}\\= a^{ -1 . 2 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
8. \(\left(y^{\frac{-5}{4}}\right)^{\frac{-2}{5}}\\= y^{ \frac{-5}{4} . (\frac{-2}{5}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
9. \(\left(x^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{2}{3} . (\frac{-1}{2}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
10. \(\left(y^{-1}\right)^{\frac{-2}{3}}\\= y^{ -1 . (\frac{-2}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
11. \(\left(x^{2}\right)^{\frac{-1}{2}}\\= x^{ 2 . (\frac{-1}{2}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
12. \(\left(q^{\frac{3}{4}}\right)^{\frac{-5}{3}}\\= q^{ \frac{3}{4} . (\frac{-5}{3}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)