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Werk uit m.b.v. de rekenregels

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

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