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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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