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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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