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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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