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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{6}}\right)^{-1}\\= x^{ \frac{-5}{6} . (-1) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
2. \(\left(y^{\frac{5}{4}}\right)^{-2}\\= y^{ \frac{5}{4} . (-2) }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
3. \(\left(q^{1}\right)^{\frac{-1}{6}}\\= q^{ 1 . (\frac{-1}{6}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
4. \(\left(a^{-2}\right)^{\frac{-1}{6}}\\= a^{ -2 . (\frac{-1}{6}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
5. \(\left(a^{\frac{1}{3}}\right)^{\frac{-2}{5}}\\= a^{ \frac{1}{3} . (\frac{-2}{5}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
6. \(\left(a^{\frac{4}{3}}\right)^{-1}\\= a^{ \frac{4}{3} . (-1) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
7. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-2}{3} . (\frac{-1}{6}) }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)
8. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{6}}\\= q^{ \frac{1}{2} . \frac{1}{6} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
9. \(\left(q^{\frac{1}{3}}\right)^{-1}\\= q^{ \frac{1}{3} . (-1) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
10. \(\left(a^{\frac{-4}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-4}{3} . \frac{1}{3} }= a^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ a^{4} }}=\frac{1}{\sqrt[9]{ a^{4} }}. \color{purple}{\frac{\sqrt[9]{ a^{5} }}{\sqrt[9]{ a^{5} }}} \\=\frac{\sqrt[9]{ a^{5} }}{a}\\---------------\)
11. \(\left(a^{\frac{1}{5}}\right)^{\frac{-4}{3}}\\= a^{ \frac{1}{5} . (\frac{-4}{3}) }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
12. \(\left(y^{\frac{1}{6}}\right)^{\frac{-1}{5}}\\= y^{ \frac{1}{6} . (\frac{-1}{5}) }= y^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ y }}=\frac{1}{\sqrt[30]{ y }}. \color{purple}{\frac{\sqrt[30]{ y^{29} }}{\sqrt[30]{ y^{29} }}} \\=\frac{\sqrt[30]{ y^{29} }}{|y|}\\---------------\)