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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{1}\right)^{\frac{-1}{3}}\\= a^{ 1 . (\frac{-1}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(\left(q^{\frac{1}{3}}\right)^{\frac{-1}{6}}\\= q^{ \frac{1}{3} . (\frac{-1}{6}) }= q^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ q }}=\frac{1}{\sqrt[18]{ q }}. \color{purple}{\frac{\sqrt[18]{ q^{17} }}{\sqrt[18]{ q^{17} }}} \\=\frac{\sqrt[18]{ q^{17} }}{|q|}\\---------------\)
3. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{3} . \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
4. \(\left(q^{\frac{-1}{3}}\right)^{1}\\= q^{ \frac{-1}{3} . 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
5. \(\left(a^{\frac{1}{2}}\right)^{\frac{5}{2}}\\= a^{ \frac{1}{2} . \frac{5}{2} }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
6. \(\left(q^{\frac{-1}{4}}\right)^{\frac{3}{5}}\\= q^{ \frac{-1}{4} . \frac{3}{5} }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
7. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)
8. \(\left(y^{\frac{-3}{5}}\right)^{2}\\= y^{ \frac{-3}{5} . 2 }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
9. \(\left(y^{\frac{4}{5}}\right)^{\frac{1}{5}}\\= y^{ \frac{4}{5} . \frac{1}{5} }= y^{\frac{4}{25}}\\=\sqrt[25]{ y^{4} }\\---------------\)
10. \(\left(a^{\frac{-3}{5}}\right)^{1}\\= a^{ \frac{-3}{5} . 1 }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
11. \(\left(x^{1}\right)^{\frac{-5}{2}}\\= x^{ 1 . (\frac{-5}{2}) }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
12. \(\left(q^{\frac{-3}{5}}\right)^{\frac{5}{6}}\\= q^{ \frac{-3}{5} . \frac{5}{6} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)