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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{2}{3}}\right)^{\frac{-3}{4}}\\= x^{ \frac{2}{3} . (\frac{-3}{4}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
2. \(\left(x^{\frac{4}{5}}\right)^{-1}\\= x^{ \frac{4}{5} . (-1) }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
3. \(\left(a^{\frac{-2}{5}}\right)^{\frac{1}{6}}\\= a^{ \frac{-2}{5} . \frac{1}{6} }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
4. \(\left(a^{-1}\right)^{\frac{-3}{2}}\\= a^{ -1 . (\frac{-3}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
5. \(\left(x^{\frac{1}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{5} . (\frac{-1}{2}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
6. \(\left(a^{-2}\right)^{-2}\\= a^{ -2 . (-2) }= a^{4}\\\\---------------\)
7. \(\left(y^{\frac{1}{4}}\right)^{\frac{-1}{6}}\\= y^{ \frac{1}{4} . (\frac{-1}{6}) }= y^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ y }}=\frac{1}{\sqrt[24]{ y }}. \color{purple}{\frac{\sqrt[24]{ y^{23} }}{\sqrt[24]{ y^{23} }}} \\=\frac{\sqrt[24]{ y^{23} }}{|y|}\\---------------\)
8. \(\left(y^{\frac{4}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{4}{3} . (\frac{-1}{3}) }= y^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ y^{4} }}=\frac{1}{\sqrt[9]{ y^{4} }}. \color{purple}{\frac{\sqrt[9]{ y^{5} }}{\sqrt[9]{ y^{5} }}} \\=\frac{\sqrt[9]{ y^{5} }}{y}\\---------------\)
9. \(\left(x^{\frac{5}{2}}\right)^{\frac{-5}{3}}\\= x^{ \frac{5}{2} . (\frac{-5}{3}) }= x^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ x^{25} }}\\=\frac{1}{|x^{4}|.\sqrt[6]{ x }}=\frac{1}{|x^{4}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{5}|}\\---------------\)
10. \(\left(x^{\frac{1}{4}}\right)^{-1}\\= x^{ \frac{1}{4} . (-1) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
11. \(\left(a^{\frac{3}{2}}\right)^{\frac{-5}{6}}\\= a^{ \frac{3}{2} . (\frac{-5}{6}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
12. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)