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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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