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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{-5}{4} . \frac{1}{2} }= x^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ x^{5} }}=\frac{1}{\sqrt[8]{ x^{5} }}. \color{purple}{\frac{\sqrt[8]{ x^{3} }}{\sqrt[8]{ x^{3} }}} \\=\frac{\sqrt[8]{ x^{3} }}{|x|}\\---------------\)
2. \(\left(y^{\frac{3}{2}}\right)^{\frac{-5}{6}}\\= y^{ \frac{3}{2} . (\frac{-5}{6}) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
3. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-1}{2} . (\frac{-1}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
4. \(\left(y^{\frac{5}{6}}\right)^{\frac{1}{6}}\\= y^{ \frac{5}{6} . \frac{1}{6} }= y^{\frac{5}{36}}\\=\sqrt[36]{ y^{5} }\\---------------\)
5. \(\left(a^{1}\right)^{\frac{-1}{2}}\\= a^{ 1 . (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
6. \(\left(a^{\frac{-5}{2}}\right)^{\frac{1}{4}}\\= a^{ \frac{-5}{2} . \frac{1}{4} }= a^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ a^{5} }}=\frac{1}{\sqrt[8]{ a^{5} }}. \color{purple}{\frac{\sqrt[8]{ a^{3} }}{\sqrt[8]{ a^{3} }}} \\=\frac{\sqrt[8]{ a^{3} }}{|a|}\\---------------\)
7. \(\left(a^{\frac{3}{5}}\right)^{\frac{-1}{4}}\\= a^{ \frac{3}{5} . (\frac{-1}{4}) }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
8. \(\left(x^{\frac{5}{6}}\right)^{\frac{-2}{5}}\\= x^{ \frac{5}{6} . (\frac{-2}{5}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
9. \(\left(x^{\frac{1}{2}}\right)^{1}\\= x^{ \frac{1}{2} . 1 }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(\left(x^{\frac{-5}{4}}\right)^{\frac{2}{5}}\\= x^{ \frac{-5}{4} . \frac{2}{5} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
11. \(\left(y^{\frac{1}{3}}\right)^{1}\\= y^{ \frac{1}{3} . 1 }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
12. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)