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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{6}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{6} . \frac{1}{2} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
2. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-1}{2} . (\frac{-2}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
3. \(\left(a^{\frac{-5}{6}}\right)^{\frac{1}{3}}\\= a^{ \frac{-5}{6} . \frac{1}{3} }= a^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ a^{5} }}=\frac{1}{\sqrt[18]{ a^{5} }}. \color{purple}{\frac{\sqrt[18]{ a^{13} }}{\sqrt[18]{ a^{13} }}} \\=\frac{\sqrt[18]{ a^{13} }}{|a|}\\---------------\)
4. \(\left(x^{\frac{-4}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-4}{3} . (\frac{-2}{3}) }= x^{\frac{8}{9}}\\=\sqrt[9]{ x^{8} }\\---------------\)
5. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
6. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{2}{3} . (\frac{-1}{3}) }= q^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ q^{2} }}=\frac{1}{\sqrt[9]{ q^{2} }}. \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q}\\---------------\)
7. \(\left(q^{-2}\right)^{1}\\= q^{ -2 . 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
8. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-5}{6} . (\frac{-5}{6}) }= x^{\frac{25}{36}}\\=\sqrt[36]{ x^{25} }\\---------------\)
9. \(\left(y^{\frac{-3}{4}}\right)^{\frac{3}{4}}\\= y^{ \frac{-3}{4} . \frac{3}{4} }= y^{\frac{-9}{16}}\\=\frac{1}{\sqrt[16]{ y^{9} }}=\frac{1}{\sqrt[16]{ y^{9} }}. \color{purple}{\frac{\sqrt[16]{ y^{7} }}{\sqrt[16]{ y^{7} }}} \\=\frac{\sqrt[16]{ y^{7} }}{|y|}\\---------------\)
10. \(\left(x^{\frac{-5}{2}}\right)^{\frac{1}{3}}\\= x^{ \frac{-5}{2} . \frac{1}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
11. \(\left(a^{\frac{3}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{3}{5} . (\frac{-1}{2}) }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
12. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{2}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)