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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{2}}\\= a^{ \frac{5}{6} . \frac{1}{2} }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
2. \(\left(y^{\frac{3}{4}}\right)^{-1}\\= y^{ \frac{3}{4} . (-1) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
3. \(\left(a^{-1}\right)^{\frac{1}{4}}\\= a^{ -1 . \frac{1}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
4. \(\left(x^{\frac{-1}{6}}\right)^{1}\\= x^{ \frac{-1}{6} . 1 }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
5. \(\left(y^{1}\right)^{\frac{-3}{5}}\\= y^{ 1 . (\frac{-3}{5}) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
6. \(\left(a^{\frac{-2}{3}}\right)^{\frac{5}{2}}\\= a^{ \frac{-2}{3} . \frac{5}{2} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
7. \(\left(a^{\frac{-1}{5}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{5} . \frac{1}{2} }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
8. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-1}{2} . (\frac{-3}{2}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
9. \(\left(a^{\frac{5}{4}}\right)^{\frac{1}{6}}\\= a^{ \frac{5}{4} . \frac{1}{6} }= a^{\frac{5}{24}}\\=\sqrt[24]{ a^{5} }\\---------------\)
10. \(\left(y^{\frac{-1}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{-1}{3} . \frac{1}{3} }= y^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ y }}=\frac{1}{\sqrt[9]{ y }}. \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y}\\---------------\)
11. \(\left(x^{\frac{-4}{3}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-4}{3} . (\frac{-1}{4}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
12. \(\left(y^{\frac{-1}{2}}\right)^{2}\\= y^{ \frac{-1}{2} . 2 }= y^{-1}\\=\frac{1}{y}\\---------------\)