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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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