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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{6}}\right)^{-1}\\= x^{ \frac{-1}{6} . (-1) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
2. \(\left(x^{\frac{5}{2}}\right)^{\frac{2}{5}}\\= x^{ \frac{5}{2} . \frac{2}{5} }= x^{1}\\\\---------------\)
3. \(\left(q^{-1}\right)^{\frac{1}{6}}\\= q^{ -1 . \frac{1}{6} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
4. \(\left(q^{\frac{5}{3}}\right)^{\frac{5}{2}}\\= q^{ \frac{5}{3} . \frac{5}{2} }= q^{\frac{25}{6}}\\=\sqrt[6]{ q^{25} }=|q^{4}|.\sqrt[6]{ q }\\---------------\)
5. \(\left(y^{\frac{5}{4}}\right)^{\frac{4}{3}}\\= y^{ \frac{5}{4} . \frac{4}{3} }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
6. \(\left(a^{\frac{-5}{4}}\right)^{\frac{-1}{5}}\\= a^{ \frac{-5}{4} . (\frac{-1}{5}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
7. \(\left(y^{\frac{1}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{5} . (\frac{-1}{2}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
8. \(\left(q^{\frac{-3}{2}}\right)^{\frac{5}{2}}\\= q^{ \frac{-3}{2} . \frac{5}{2} }= q^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ q^{15} }}\\=\frac{1}{|q^{3}|.\sqrt[4]{ q^{3} }}=\frac{1}{|q^{3}|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{4}|}\\---------------\)
9. \(\left(y^{\frac{2}{5}}\right)^{\frac{5}{6}}\\= y^{ \frac{2}{5} . \frac{5}{6} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
10. \(\left(a^{\frac{1}{6}}\right)^{\frac{5}{4}}\\= a^{ \frac{1}{6} . \frac{5}{4} }= a^{\frac{5}{24}}\\=\sqrt[24]{ a^{5} }\\---------------\)
11. \(\left(y^{\frac{1}{5}}\right)^{\frac{-3}{2}}\\= y^{ \frac{1}{5} . (\frac{-3}{2}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
12. \(\left(y^{\frac{1}{6}}\right)^{-2}\\= y^{ \frac{1}{6} . (-2) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)