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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-3}{2}}\\= y^{ \frac{-2}{3} . (\frac{-3}{2}) }= y^{1}\\\\---------------\)
2. \(\left(q^{\frac{-3}{5}}\right)^{\frac{5}{6}}\\= q^{ \frac{-3}{5} . \frac{5}{6} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\left(q^{-1}\right)^{-1}\\= q^{ -1 . (-1) }= q^{1}\\\\---------------\)
4. \(\left(q^{\frac{1}{6}}\right)^{\frac{1}{3}}\\= q^{ \frac{1}{6} . \frac{1}{3} }= q^{\frac{1}{18}}\\=\sqrt[18]{ q }\\---------------\)
5. \(\left(y^{\frac{5}{2}}\right)^{-1}\\= y^{ \frac{5}{2} . (-1) }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
6. \(\left(q^{\frac{5}{4}}\right)^{\frac{1}{6}}\\= q^{ \frac{5}{4} . \frac{1}{6} }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
7. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
8. \(\left(x^{\frac{1}{4}}\right)^{\frac{1}{6}}\\= x^{ \frac{1}{4} . \frac{1}{6} }= x^{\frac{1}{24}}\\=\sqrt[24]{ x }\\---------------\)
9. \(\left(x^{-1}\right)^{-2}\\= x^{ -1 . (-2) }= x^{2}\\\\---------------\)
10. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
11. \(\left(a^{-1}\right)^{\frac{1}{2}}\\= a^{ -1 . \frac{1}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
12. \(\left(a^{\frac{1}{3}}\right)^{-1}\\= a^{ \frac{1}{3} . (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)