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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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