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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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