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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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