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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{-2}\right)^{\frac{-2}{3}}\\= x^{ -2 . (\frac{-2}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
2. \(\left(y^{\frac{3}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{3}{2} . (\frac{-1}{2}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
3. \(\left(q^{-1}\right)^{\frac{5}{6}}\\= q^{ -1 . \frac{5}{6} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
4. \(\left(x^{\frac{-5}{3}}\right)^{1}\\= x^{ \frac{-5}{3} . 1 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
5. \(\left(a^{1}\right)^{\frac{-1}{5}}\\= a^{ 1 . (\frac{-1}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
6. \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{6} . \frac{1}{2} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
7. \(\left(x^{\frac{-1}{3}}\right)^{\frac{3}{2}}\\= x^{ \frac{-1}{3} . \frac{3}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\left(y^{\frac{4}{5}}\right)^{1}\\= y^{ \frac{4}{5} . 1 }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
9. \(\left(y^{-2}\right)^{\frac{-5}{3}}\\= y^{ -2 . (\frac{-5}{3}) }= y^{\frac{10}{3}}\\=\sqrt[3]{ y^{10} }=y^{3}.\sqrt[3]{ y }\\---------------\)
10. \(\left(a^{\frac{1}{5}}\right)^{\frac{-2}{5}}\\= a^{ \frac{1}{5} . (\frac{-2}{5}) }= a^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ a^{2} }}=\frac{1}{\sqrt[25]{ a^{2} }}. \color{purple}{\frac{\sqrt[25]{ a^{23} }}{\sqrt[25]{ a^{23} }}} \\=\frac{\sqrt[25]{ a^{23} }}{a}\\---------------\)
11. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-5}{6} . (\frac{-1}{5}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
12. \(\left(q^{\frac{5}{3}}\right)^{1}\\= q^{ \frac{5}{3} . 1 }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)