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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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