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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{2}{3}}\right)^{\frac{-1}{6}}\\= x^{ \frac{2}{3} . (\frac{-1}{6}) }= x^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ x }}=\frac{1}{\sqrt[9]{ x }}. \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x}\\---------------\)
2. \(\left(y^{\frac{-3}{4}}\right)^{\frac{1}{6}}\\= y^{ \frac{-3}{4} . \frac{1}{6} }= y^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ y }}=\frac{1}{\sqrt[8]{ y }}. \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y|}\\---------------\)
3. \(\left(x^{\frac{1}{6}}\right)^{\frac{-4}{5}}\\= x^{ \frac{1}{6} . (\frac{-4}{5}) }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
4. \(\left(q^{\frac{-1}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{4} . \frac{1}{2} }= q^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ q }}=\frac{1}{\sqrt[8]{ q }}. \color{purple}{\frac{\sqrt[8]{ q^{7} }}{\sqrt[8]{ q^{7} }}} \\=\frac{\sqrt[8]{ q^{7} }}{|q|}\\---------------\)
5. \(\left(x^{2}\right)^{\frac{-3}{2}}\\= x^{ 2 . (\frac{-3}{2}) }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)
6. \(\left(x^{\frac{2}{3}}\right)^{\frac{-1}{4}}\\= x^{ \frac{2}{3} . (\frac{-1}{4}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
7. \(\left(x^{\frac{-3}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-3}{2} . (\frac{-1}{2}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
8. \(\left(a^{\frac{-3}{4}}\right)^{\frac{1}{4}}\\= a^{ \frac{-3}{4} . \frac{1}{4} }= a^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ a^{3} }}=\frac{1}{\sqrt[16]{ a^{3} }}. \color{purple}{\frac{\sqrt[16]{ a^{13} }}{\sqrt[16]{ a^{13} }}} \\=\frac{\sqrt[16]{ a^{13} }}{|a|}\\---------------\)
9. \(\left(x^{-1}\right)^{\frac{-3}{4}}\\= x^{ -1 . (\frac{-3}{4}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
10. \(\left(q^{\frac{-3}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{-3}{2} . \frac{1}{3} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
11. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-1}{5} . (\frac{-5}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
12. \(\left(x^{\frac{5}{6}}\right)^{\frac{-5}{2}}\\= x^{ \frac{5}{6} . (\frac{-5}{2}) }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)