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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-5}{6}}\right)^{\frac{5}{6}}\\= a^{ \frac{-5}{6} . \frac{5}{6} }= a^{\frac{-25}{36}}\\=\frac{1}{\sqrt[36]{ a^{25} }}=\frac{1}{\sqrt[36]{ a^{25} }}. \color{purple}{\frac{\sqrt[36]{ a^{11} }}{\sqrt[36]{ a^{11} }}} \\=\frac{\sqrt[36]{ a^{11} }}{|a|}\\---------------\)
2. \(\left(y^{\frac{2}{5}}\right)^{\frac{-4}{3}}\\= y^{ \frac{2}{5} . (\frac{-4}{3}) }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
3. \(\left(q^{\frac{-1}{6}}\right)^{-1}\\= q^{ \frac{-1}{6} . (-1) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
4. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
5. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-5}{6} . (\frac{-5}{4}) }= q^{\frac{25}{24}}\\=\sqrt[24]{ q^{25} }=|q|.\sqrt[24]{ q }\\---------------\)
6. \(\left(y^{\frac{-1}{2}}\right)^{\frac{4}{5}}\\= y^{ \frac{-1}{2} . \frac{4}{5} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
7. \(\left(y^{\frac{-1}{5}}\right)^{\frac{5}{2}}\\= y^{ \frac{-1}{5} . \frac{5}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
8. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{2} . (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
9. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{2}{3} . (\frac{-1}{3}) }= y^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ y^{2} }}=\frac{1}{\sqrt[9]{ y^{2} }}. \color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y}\\---------------\)
10. \(\left(q^{\frac{3}{2}}\right)^{1}\\= q^{ \frac{3}{2} . 1 }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
11. \(\left(a^{\frac{-5}{2}}\right)^{1}\\= a^{ \frac{-5}{2} . 1 }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
12. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{1}{2} . (\frac{-1}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)