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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{1}\right)^{\frac{-3}{2}}\\= x^{ 1 . (\frac{-3}{2}) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
2. \(\left(q^{\frac{-1}{5}}\right)^{\frac{1}{6}}\\= q^{ \frac{-1}{5} . \frac{1}{6} }= q^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ q }}=\frac{1}{\sqrt[30]{ q }}. \color{purple}{\frac{\sqrt[30]{ q^{29} }}{\sqrt[30]{ q^{29} }}} \\=\frac{\sqrt[30]{ q^{29} }}{|q|}\\---------------\)
3. \(\left(x^{-1}\right)^{\frac{-5}{4}}\\= x^{ -1 . (\frac{-5}{4}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
4. \(\left(a^{\frac{-2}{3}}\right)^{\frac{3}{5}}\\= a^{ \frac{-2}{3} . \frac{3}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
5. \(\left(x^{-1}\right)^{\frac{1}{2}}\\= x^{ -1 . \frac{1}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
6. \(\left(x^{\frac{1}{2}}\right)^{\frac{-1}{4}}\\= x^{ \frac{1}{2} . (\frac{-1}{4}) }= x^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ x }}=\frac{1}{\sqrt[8]{ x }}. \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x|}\\---------------\)
7. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-1}{2} . (\frac{-1}{3}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
8. \(\left(a^{1}\right)^{\frac{-1}{6}}\\= a^{ 1 . (\frac{-1}{6}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
9. \(\left(a^{-1}\right)^{\frac{-1}{6}}\\= a^{ -1 . (\frac{-1}{6}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
10. \(\left(y^{\frac{-4}{5}}\right)^{\frac{2}{5}}\\= y^{ \frac{-4}{5} . \frac{2}{5} }= y^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ y^{8} }}=\frac{1}{\sqrt[25]{ y^{8} }}. \color{purple}{\frac{\sqrt[25]{ y^{17} }}{\sqrt[25]{ y^{17} }}} \\=\frac{\sqrt[25]{ y^{17} }}{y}\\---------------\)
11. \(\left(a^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{2} . \frac{1}{2} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
12. \(\left(a^{\frac{2}{5}}\right)^{\frac{3}{2}}\\= a^{ \frac{2}{5} . \frac{3}{2} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)