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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{1}\right)^{\frac{-5}{2}}\\= a^{ 1 . (\frac{-5}{2}) }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
2. \(\left(a^{\frac{5}{6}}\right)^{1}\\= a^{ \frac{5}{6} . 1 }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
3. \(\left(y^{\frac{-5}{4}}\right)^{1}\\= y^{ \frac{-5}{4} . 1 }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
4. \(\left(y^{\frac{-5}{4}}\right)^{\frac{1}{6}}\\= y^{ \frac{-5}{4} . \frac{1}{6} }= y^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ y^{5} }}=\frac{1}{\sqrt[24]{ y^{5} }}. \color{purple}{\frac{\sqrt[24]{ y^{19} }}{\sqrt[24]{ y^{19} }}} \\=\frac{\sqrt[24]{ y^{19} }}{|y|}\\---------------\)
5. \(\left(x^{\frac{1}{2}}\right)^{\frac{-5}{3}}\\= x^{ \frac{1}{2} . (\frac{-5}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
6. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-3}{5} . (\frac{-5}{3}) }= y^{1}\\\\---------------\)
7. \(\left(y^{\frac{1}{3}}\right)^{\frac{5}{2}}\\= y^{ \frac{1}{3} . \frac{5}{2} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
8. \(\left(q^{2}\right)^{\frac{-1}{6}}\\= q^{ 2 . (\frac{-1}{6}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
9. \(\left(y^{1}\right)^{\frac{1}{5}}\\= y^{ 1 . \frac{1}{5} }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
10. \(\left(a^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= a^{ \frac{-5}{6} . \frac{1}{2} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
11. \(\left(x^{\frac{2}{5}}\right)^{\frac{5}{4}}\\= x^{ \frac{2}{5} . \frac{5}{4} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\left(a^{\frac{5}{2}}\right)^{\frac{-5}{2}}\\= a^{ \frac{5}{2} . (\frac{-5}{2}) }= a^{\frac{-25}{4}}\\=\frac{1}{\sqrt[4]{ a^{25} }}\\=\frac{1}{|a^{6}|.\sqrt[4]{ a }}=\frac{1}{|a^{6}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{7}|}\\---------------\)