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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{6}}\\= q^{ \frac{1}{2} . \frac{1}{6} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
2. \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-2}{3} . \frac{1}{3} }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)
3. \(\left(y^{\frac{5}{4}}\right)^{\frac{-5}{4}}\\= y^{ \frac{5}{4} . (\frac{-5}{4}) }= y^{\frac{-25}{16}}\\=\frac{1}{\sqrt[16]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[16]{ y^{9} }}=\frac{1}{|y|.\sqrt[16]{ y^{9} }} \color{purple}{\frac{\sqrt[16]{ y^{7} }}{\sqrt[16]{ y^{7} }}} \\=\frac{\sqrt[16]{ y^{7} }}{|y^{2}|}\\---------------\)
4. \(\left(y^{\frac{5}{6}}\right)^{\frac{-3}{2}}\\= y^{ \frac{5}{6} . (\frac{-3}{2}) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
5. \(\left(q^{\frac{-2}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{-2}{5} . \frac{1}{3} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
6. \(\left(a^{\frac{-1}{2}}\right)^{\frac{5}{2}}\\= a^{ \frac{-1}{2} . \frac{5}{2} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
7. \(\left(y^{\frac{1}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{1}{3} . \frac{2}{3} }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
8. \(\left(q^{\frac{2}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{2}{5} . \frac{1}{3} }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
9. \(\left(x^{\frac{3}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{3}{5} . (\frac{-1}{2}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
10. \(\left(x^{\frac{5}{6}}\right)^{-1}\\= x^{ \frac{5}{6} . (-1) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
11. \(\left(x^{2}\right)^{\frac{-3}{2}}\\= x^{ 2 . (\frac{-3}{2}) }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)
12. \(\left(a^{\frac{-1}{6}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-1}{6} . (\frac{-4}{3}) }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)