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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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