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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{4} . (\frac{-1}{2}) }= y^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ y }}=\frac{1}{\sqrt[8]{ y }}. \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y|}\\---------------\)
2. \(\left(y^{\frac{5}{3}}\right)^{\frac{5}{6}}\\= y^{ \frac{5}{3} . \frac{5}{6} }= y^{\frac{25}{18}}\\=\sqrt[18]{ y^{25} }=|y|.\sqrt[18]{ y^{7} }\\---------------\)
3. \(\left(q^{-1}\right)^{\frac{-1}{2}}\\= q^{ -1 . (\frac{-1}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
4. \(\left(y^{\frac{3}{2}}\right)^{\frac{3}{2}}\\= y^{ \frac{3}{2} . \frac{3}{2} }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
5. \(\left(x^{\frac{-3}{2}}\right)^{\frac{1}{6}}\\= x^{ \frac{-3}{2} . \frac{1}{6} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
6. \(\left(a^{2}\right)^{\frac{3}{2}}\\= a^{ 2 . \frac{3}{2} }= a^{3}\\\\---------------\)
7. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-5}{3} . (\frac{-5}{2}) }= a^{\frac{25}{6}}\\=\sqrt[6]{ a^{25} }=|a^{4}|.\sqrt[6]{ a }\\---------------\)
8. \(\left(q^{\frac{-1}{6}}\right)^{-1}\\= q^{ \frac{-1}{6} . (-1) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
9. \(\left(x^{\frac{-3}{5}}\right)^{\frac{1}{6}}\\= x^{ \frac{-3}{5} . \frac{1}{6} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
10. \(\left(y^{\frac{5}{4}}\right)^{\frac{5}{6}}\\= y^{ \frac{5}{4} . \frac{5}{6} }= y^{\frac{25}{24}}\\=\sqrt[24]{ y^{25} }=|y|.\sqrt[24]{ y }\\---------------\)
11. \(\left(a^{\frac{-1}{3}}\right)^{2}\\= a^{ \frac{-1}{3} . 2 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
12. \(\left(x^{-1}\right)^{-2}\\= x^{ -1 . (-2) }= x^{2}\\\\---------------\)