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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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