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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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