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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{2}}\right)^{\frac{1}{6}}\\= a^{ \frac{1}{2} . \frac{1}{6} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
2. \(\left(x^{\frac{4}{5}}\right)^{\frac{-1}{5}}\\= x^{ \frac{4}{5} . (\frac{-1}{5}) }= x^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ x^{4} }}=\frac{1}{\sqrt[25]{ x^{4} }}. \color{purple}{\frac{\sqrt[25]{ x^{21} }}{\sqrt[25]{ x^{21} }}} \\=\frac{\sqrt[25]{ x^{21} }}{x}\\---------------\)
3. \(\left(x^{\frac{-1}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{5} . \frac{1}{2} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
4. \(\left(q^{\frac{2}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{2}{3} . \frac{2}{3} }= q^{\frac{4}{9}}\\=\sqrt[9]{ q^{4} }\\---------------\)
5. \(\left(x^{\frac{5}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{5}{2} . (\frac{-2}{3}) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
6. \(\left(a^{\frac{5}{4}}\right)^{\frac{5}{2}}\\= a^{ \frac{5}{4} . \frac{5}{2} }= a^{\frac{25}{8}}\\=\sqrt[8]{ a^{25} }=|a^{3}|.\sqrt[8]{ a }\\---------------\)
7. \(\left(y^{1}\right)^{\frac{-1}{2}}\\= y^{ 1 . (\frac{-1}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
8. \(\left(a^{\frac{-2}{5}}\right)^{\frac{5}{2}}\\= a^{ \frac{-2}{5} . \frac{5}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
9. \(\left(a^{2}\right)^{1}\\= a^{ 2 . 1 }= a^{2}\\\\---------------\)
10. \(\left(q^{\frac{-2}{5}}\right)^{\frac{1}{4}}\\= q^{ \frac{-2}{5} . \frac{1}{4} }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
11. \(\left(a^{\frac{4}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{4}{5} . \frac{1}{3} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
12. \(\left(a^{\frac{-5}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-5}{2} . (\frac{-1}{2}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)