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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{3}}\right)^{\frac{5}{6}}\\= x^{ \frac{-5}{3} . \frac{5}{6} }= x^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ x^{25} }}\\=\frac{1}{|x|.\sqrt[18]{ x^{7} }}=\frac{1}{|x|.\sqrt[18]{ x^{7} }} \color{purple}{\frac{\sqrt[18]{ x^{11} }}{\sqrt[18]{ x^{11} }}} \\=\frac{\sqrt[18]{ x^{11} }}{|x^{2}|}\\---------------\)
2. \(\left(x^{\frac{-1}{3}}\right)^{1}\\= x^{ \frac{-1}{3} . 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
3. \(\left(x^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= x^{ \frac{-1}{2} . \frac{2}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
4. \(\left(y^{\frac{1}{3}}\right)^{\frac{-4}{3}}\\= y^{ \frac{1}{3} . (\frac{-4}{3}) }= y^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ y^{4} }}=\frac{1}{\sqrt[9]{ y^{4} }}. \color{purple}{\frac{\sqrt[9]{ y^{5} }}{\sqrt[9]{ y^{5} }}} \\=\frac{\sqrt[9]{ y^{5} }}{y}\\---------------\)
5. \(\left(x^{-1}\right)^{1}\\= x^{ -1 . 1 }= x^{-1}\\=\frac{1}{x}\\---------------\)
6. \(\left(a^{\frac{-2}{5}}\right)^{\frac{5}{2}}\\= a^{ \frac{-2}{5} . \frac{5}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
7. \(\left(x^{\frac{-2}{5}}\right)^{-2}\\= x^{ \frac{-2}{5} . (-2) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
8. \(\left(y^{\frac{4}{5}}\right)^{\frac{1}{6}}\\= y^{ \frac{4}{5} . \frac{1}{6} }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
9. \(\left(a^{\frac{4}{3}}\right)^{-1}\\= a^{ \frac{4}{3} . (-1) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
10. \(\left(q^{\frac{2}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{2}{3} . \frac{2}{3} }= q^{\frac{4}{9}}\\=\sqrt[9]{ q^{4} }\\---------------\)
11. \(\left(q^{\frac{4}{3}}\right)^{\frac{-2}{5}}\\= q^{ \frac{4}{3} . (\frac{-2}{5}) }= q^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ q^{8} }}=\frac{1}{\sqrt[15]{ q^{8} }}. \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q}\\---------------\)
12. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{3} . \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)