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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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