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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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