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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{2}}\right)^{-1}\\= a^{ \frac{5}{2} . (-1) }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
2. \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{4}}\\= q^{ \frac{1}{4} . (\frac{-1}{4}) }= q^{\frac{-1}{16}}\\=\frac{1}{\sqrt[16]{ q }}=\frac{1}{\sqrt[16]{ q }}. \color{purple}{\frac{\sqrt[16]{ q^{15} }}{\sqrt[16]{ q^{15} }}} \\=\frac{\sqrt[16]{ q^{15} }}{|q|}\\---------------\)
3. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-1}{5} . (\frac{-1}{2}) }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
4. \(\left(a^{-1}\right)^{\frac{-2}{3}}\\= a^{ -1 . (\frac{-2}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
5. \(\left(q^{\frac{5}{3}}\right)^{-1}\\= q^{ \frac{5}{3} . (-1) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
6. \(\left(x^{\frac{-1}{3}}\right)^{\frac{3}{2}}\\= x^{ \frac{-1}{3} . \frac{3}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
7. \(\left(q^{\frac{5}{3}}\right)^{\frac{5}{2}}\\= q^{ \frac{5}{3} . \frac{5}{2} }= q^{\frac{25}{6}}\\=\sqrt[6]{ q^{25} }=|q^{4}|.\sqrt[6]{ q }\\---------------\)
8. \(\left(y^{-1}\right)^{1}\\= y^{ -1 . 1 }= y^{-1}\\=\frac{1}{y}\\---------------\)
9. \(\left(x^{\frac{1}{2}}\right)^{\frac{1}{6}}\\= x^{ \frac{1}{2} . \frac{1}{6} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
10. \(\left(a^{\frac{1}{2}}\right)^{\frac{-5}{6}}\\= a^{ \frac{1}{2} . (\frac{-5}{6}) }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
11. \(\left(q^{\frac{5}{6}}\right)^{\frac{-1}{3}}\\= q^{ \frac{5}{6} . (\frac{-1}{3}) }= q^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ q^{5} }}=\frac{1}{\sqrt[18]{ q^{5} }}. \color{purple}{\frac{\sqrt[18]{ q^{13} }}{\sqrt[18]{ q^{13} }}} \\=\frac{\sqrt[18]{ q^{13} }}{|q|}\\---------------\)
12. \(\left(y^{\frac{-4}{5}}\right)^{\frac{1}{4}}\\= y^{ \frac{-4}{5} . \frac{1}{4} }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)