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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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