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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{2}}\right)^{1}\\= x^{ \frac{5}{2} . 1 }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
2. \(\left(y^{\frac{-1}{3}}\right)^{1}\\= y^{ \frac{-1}{3} . 1 }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
3. \(\left(y^{\frac{-4}{5}}\right)^{1}\\= y^{ \frac{-4}{5} . 1 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
4. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-2}{3} . \frac{1}{2} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
5. \(\left(y^{\frac{1}{3}}\right)^{\frac{-5}{6}}\\= y^{ \frac{1}{3} . (\frac{-5}{6}) }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
6. \(\left(y^{\frac{-5}{2}}\right)^{\frac{3}{2}}\\= y^{ \frac{-5}{2} . \frac{3}{2} }= y^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ y^{15} }}\\=\frac{1}{|y^{3}|.\sqrt[4]{ y^{3} }}=\frac{1}{|y^{3}|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{4}|}\\---------------\)
7. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{4}}\\= x^{ \frac{-1}{2} . \frac{1}{4} }= x^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ x }}=\frac{1}{\sqrt[8]{ x }}. \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x|}\\---------------\)
8. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-2}{5}}\\= x^{ \frac{-1}{2} . (\frac{-2}{5}) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
9. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-2}{5} . (\frac{-1}{3}) }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
10. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-2}{3} . (\frac{-4}{3}) }= a^{\frac{8}{9}}\\=\sqrt[9]{ a^{8} }\\---------------\)
11. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{6}}\\= x^{ \frac{-2}{3} . \frac{1}{6} }= x^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ x }}=\frac{1}{\sqrt[9]{ x }}. \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x}\\---------------\)
12. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{2} . \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)