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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-2}{3} . (\frac{-1}{2}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
2. \(\left(y^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{3} . \frac{1}{2} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
3. \(\left(q^{\frac{-5}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{-5}{2} . \frac{1}{2} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
4. \(\left(y^{\frac{-1}{6}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{6} . \frac{1}{2} }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
5. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-1}{3} . (\frac{-5}{6}) }= y^{\frac{5}{18}}\\=\sqrt[18]{ y^{5} }\\---------------\)
6. \(\left(q^{\frac{5}{4}}\right)^{\frac{-1}{2}}\\= q^{ \frac{5}{4} . (\frac{-1}{2}) }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
7. \(\left(a^{\frac{-4}{3}}\right)^{1}\\= a^{ \frac{-4}{3} . 1 }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
8. \(\left(y^{\frac{1}{5}}\right)^{\frac{-3}{2}}\\= y^{ \frac{1}{5} . (\frac{-3}{2}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
9. \(\left(y^{\frac{1}{2}}\right)^{\frac{5}{6}}\\= y^{ \frac{1}{2} . \frac{5}{6} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
10. \(\left(x^{\frac{5}{2}}\right)^{\frac{5}{6}}\\= x^{ \frac{5}{2} . \frac{5}{6} }= x^{\frac{25}{12}}\\=\sqrt[12]{ x^{25} }=|x^{2}|.\sqrt[12]{ x }\\---------------\)
11. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
12. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{1}{2} . \frac{1}{3} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)