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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{-1}\right)^{\frac{-2}{3}}\\= y^{ -1 . (\frac{-2}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
2. \(\left(y^{\frac{5}{6}}\right)^{\frac{1}{5}}\\= y^{ \frac{5}{6} . \frac{1}{5} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
3. \(\left(y^{\frac{1}{5}}\right)^{\frac{5}{4}}\\= y^{ \frac{1}{5} . \frac{5}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
4. \(\left(x^{\frac{2}{3}}\right)^{\frac{-2}{5}}\\= x^{ \frac{2}{3} . (\frac{-2}{5}) }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
5. \(\left(y^{1}\right)^{\frac{3}{4}}\\= y^{ 1 . \frac{3}{4} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
6. \(\left(a^{\frac{5}{3}}\right)^{\frac{4}{5}}\\= a^{ \frac{5}{3} . \frac{4}{5} }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
7. \(\left(q^{\frac{2}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{2}{5} . (\frac{-1}{2}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
8. \(\left(y^{\frac{-1}{3}}\right)^{-2}\\= y^{ \frac{-1}{3} . (-2) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
9. \(\left(y^{1}\right)^{\frac{-4}{5}}\\= y^{ 1 . (\frac{-4}{5}) }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
10. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-3}{5} . (\frac{-3}{5}) }= y^{\frac{9}{25}}\\=\sqrt[25]{ y^{9} }\\---------------\)
11. \(\left(q^{\frac{1}{4}}\right)^{\frac{1}{6}}\\= q^{ \frac{1}{4} . \frac{1}{6} }= q^{\frac{1}{24}}\\=\sqrt[24]{ q }\\---------------\)
12. \(\left(q^{2}\right)^{\frac{2}{5}}\\= q^{ 2 . \frac{2}{5} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)