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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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