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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-5}{3}}\right)^{\frac{5}{2}}\\= a^{ \frac{-5}{3} . \frac{5}{2} }= a^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ a^{25} }}\\=\frac{1}{|a^{4}|.\sqrt[6]{ a }}=\frac{1}{|a^{4}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{5}|}\\---------------\)
2. \(\left(y^{\frac{-1}{4}}\right)^{\frac{2}{5}}\\= y^{ \frac{-1}{4} . \frac{2}{5} }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
3. \(\left(x^{\frac{4}{5}}\right)^{\frac{3}{5}}\\= x^{ \frac{4}{5} . \frac{3}{5} }= x^{\frac{12}{25}}\\=\sqrt[25]{ x^{12} }\\---------------\)
4. \(\left(x^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{2} . (\frac{-2}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
5. \(\left(q^{1}\right)^{\frac{-5}{2}}\\= q^{ 1 . (\frac{-5}{2}) }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
6. \(\left(x^{\frac{3}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{3}{2} . (\frac{-2}{3}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
7. \(\left(a^{\frac{4}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{4}{3} . \frac{1}{5} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
8. \(\left(a^{\frac{1}{6}}\right)^{\frac{-5}{6}}\\= a^{ \frac{1}{6} . (\frac{-5}{6}) }= a^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ a^{5} }}=\frac{1}{\sqrt[36]{ a^{5} }}. \color{purple}{\frac{\sqrt[36]{ a^{31} }}{\sqrt[36]{ a^{31} }}} \\=\frac{\sqrt[36]{ a^{31} }}{|a|}\\---------------\)
9. \(\left(q^{\frac{1}{2}}\right)^{1}\\= q^{ \frac{1}{2} . 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-5}{6}}\\= a^{ \frac{-3}{4} . (\frac{-5}{6}) }= a^{\frac{5}{8}}\\=\sqrt[8]{ a^{5} }\\---------------\)
11. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-4}{5} . (\frac{-5}{6}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-1}{2} . (\frac{-5}{2}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)