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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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