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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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