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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{-1}\right)^{\frac{5}{4}}\\= x^{ -1 . \frac{5}{4} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
2. \(\left(q^{\frac{-5}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{-5}{2} . \frac{2}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
3. \(\left(a^{\frac{-1}{2}}\right)^{-1}\\= a^{ \frac{-1}{2} . (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
4. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-4}{3} . (\frac{-2}{5}) }= q^{\frac{8}{15}}\\=\sqrt[15]{ q^{8} }\\---------------\)
5. \(\left(x^{\frac{4}{5}}\right)^{\frac{-1}{5}}\\= x^{ \frac{4}{5} . (\frac{-1}{5}) }= x^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ x^{4} }}=\frac{1}{\sqrt[25]{ x^{4} }}. \color{purple}{\frac{\sqrt[25]{ x^{21} }}{\sqrt[25]{ x^{21} }}} \\=\frac{\sqrt[25]{ x^{21} }}{x}\\---------------\)
6. \(\left(a^{1}\right)^{\frac{3}{5}}\\= a^{ 1 . \frac{3}{5} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
7. \(\left(a^{\frac{5}{6}}\right)^{\frac{5}{3}}\\= a^{ \frac{5}{6} . \frac{5}{3} }= a^{\frac{25}{18}}\\=\sqrt[18]{ a^{25} }=|a|.\sqrt[18]{ a^{7} }\\---------------\)
8. \(\left(q^{\frac{1}{4}}\right)^{\frac{-2}{5}}\\= q^{ \frac{1}{4} . (\frac{-2}{5}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
9. \(\left(q^{-1}\right)^{\frac{1}{6}}\\= q^{ -1 . \frac{1}{6} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
10. \(\left(a^{\frac{-5}{6}}\right)^{\frac{2}{5}}\\= a^{ \frac{-5}{6} . \frac{2}{5} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
11. \(\left(x^{\frac{-1}{3}}\right)^{\frac{5}{6}}\\= x^{ \frac{-1}{3} . \frac{5}{6} }= x^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ x^{5} }}=\frac{1}{\sqrt[18]{ x^{5} }}. \color{purple}{\frac{\sqrt[18]{ x^{13} }}{\sqrt[18]{ x^{13} }}} \\=\frac{\sqrt[18]{ x^{13} }}{|x|}\\---------------\)
12. \(\left(q^{\frac{5}{6}}\right)^{\frac{5}{2}}\\= q^{ \frac{5}{6} . \frac{5}{2} }= q^{\frac{25}{12}}\\=\sqrt[12]{ q^{25} }=|q^{2}|.\sqrt[12]{ q }\\---------------\)