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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{2}}\right)^{\frac{4}{5}}\\= a^{ \frac{1}{2} . \frac{4}{5} }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
2. \(\left(a^{1}\right)^{\frac{2}{3}}\\= a^{ 1 . \frac{2}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
3. \(\left(x^{\frac{-1}{6}}\right)^{\frac{1}{3}}\\= x^{ \frac{-1}{6} . \frac{1}{3} }= x^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ x }}=\frac{1}{\sqrt[18]{ x }}. \color{purple}{\frac{\sqrt[18]{ x^{17} }}{\sqrt[18]{ x^{17} }}} \\=\frac{\sqrt[18]{ x^{17} }}{|x|}\\---------------\)
4. \(\left(a^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{2} . \frac{1}{2} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
5. \(\left(a^{\frac{-5}{4}}\right)^{-1}\\= a^{ \frac{-5}{4} . (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
6. \(\left(q^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{1}{2} . (\frac{-2}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\left(a^{\frac{-1}{2}}\right)^{1}\\= a^{ \frac{-1}{2} . 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
8. \(\left(a^{\frac{1}{5}}\right)^{\frac{-5}{6}}\\= a^{ \frac{1}{5} . (\frac{-5}{6}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
9. \(\left(y^{\frac{4}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{4}{5} . (\frac{-1}{2}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
10. \(\left(a^{\frac{3}{4}}\right)^{\frac{-1}{2}}\\= a^{ \frac{3}{4} . (\frac{-1}{2}) }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)
11. \(\left(y^{\frac{3}{5}}\right)^{-1}\\= y^{ \frac{3}{5} . (-1) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
12. \(\left(y^{2}\right)^{\frac{2}{3}}\\= y^{ 2 . \frac{2}{3} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)