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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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