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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-3}{4}}\right)^{1}\\= y^{ \frac{-3}{4} . 1 }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
2. \(\left(y^{\frac{1}{2}}\right)^{1}\\= y^{ \frac{1}{2} . 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
3. \(\left(a^{\frac{2}{5}}\right)^{-1}\\= a^{ \frac{2}{5} . (-1) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
4. \(\left(x^{\frac{-1}{4}}\right)^{1}\\= x^{ \frac{-1}{4} . 1 }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
5. \(\left(y^{-1}\right)^{\frac{1}{6}}\\= y^{ -1 . \frac{1}{6} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
6. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-2}{3} . (\frac{-4}{3}) }= a^{\frac{8}{9}}\\=\sqrt[9]{ a^{8} }\\---------------\)
7. \(\left(y^{1}\right)^{\frac{-1}{3}}\\= y^{ 1 . (\frac{-1}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
8. \(\left(x^{\frac{1}{3}}\right)^{2}\\= x^{ \frac{1}{3} . 2 }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
9. \(\left(x^{\frac{5}{4}}\right)^{\frac{1}{3}}\\= x^{ \frac{5}{4} . \frac{1}{3} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
10. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-3}{4} . (\frac{-1}{2}) }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)
11. \(\left(a^{\frac{4}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{4}{5} . \frac{1}{3} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
12. \(\left(x^{\frac{-5}{6}}\right)^{\frac{5}{6}}\\= x^{ \frac{-5}{6} . \frac{5}{6} }= x^{\frac{-25}{36}}\\=\frac{1}{\sqrt[36]{ x^{25} }}=\frac{1}{\sqrt[36]{ x^{25} }}. \color{purple}{\frac{\sqrt[36]{ x^{11} }}{\sqrt[36]{ x^{11} }}} \\=\frac{\sqrt[36]{ x^{11} }}{|x|}\\---------------\)