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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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