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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{3}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{3}{2} . \frac{1}{3} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
2. \(\left(x^{1}\right)^{\frac{5}{6}}\\= x^{ 1 . \frac{5}{6} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
3. \(\left(a^{\frac{1}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{1}{5} . (\frac{-3}{5}) }= a^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ a^{3} }}=\frac{1}{\sqrt[25]{ a^{3} }}. \color{purple}{\frac{\sqrt[25]{ a^{22} }}{\sqrt[25]{ a^{22} }}} \\=\frac{\sqrt[25]{ a^{22} }}{a}\\---------------\)
4. \(\left(y^{1}\right)^{-1}\\= y^{ 1 . (-1) }= y^{-1}\\=\frac{1}{y}\\---------------\)
5. \(\left(y^{\frac{3}{2}}\right)^{\frac{5}{2}}\\= y^{ \frac{3}{2} . \frac{5}{2} }= y^{\frac{15}{4}}\\=\sqrt[4]{ y^{15} }=|y^{3}|.\sqrt[4]{ y^{3} }\\---------------\)
6. \(\left(q^{-1}\right)^{\frac{-1}{4}}\\= q^{ -1 . (\frac{-1}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
7. \(\left(q^{\frac{1}{6}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{6} . (\frac{-1}{3}) }= q^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ q }}=\frac{1}{\sqrt[18]{ q }}. \color{purple}{\frac{\sqrt[18]{ q^{17} }}{\sqrt[18]{ q^{17} }}} \\=\frac{\sqrt[18]{ q^{17} }}{|q|}\\---------------\)
8. \(\left(q^{-2}\right)^{\frac{-3}{4}}\\= q^{ -2 . (\frac{-3}{4}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
9. \(\left(x^{\frac{4}{3}}\right)^{-1}\\= x^{ \frac{4}{3} . (-1) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
10. \(\left(x^{-1}\right)^{1}\\= x^{ -1 . 1 }= x^{-1}\\=\frac{1}{x}\\---------------\)
11. \(\left(x^{\frac{1}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{5} . \frac{1}{2} }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
12. \(\left(x^{-1}\right)^{\frac{1}{2}}\\= x^{ -1 . \frac{1}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)