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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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