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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{5}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{5}{2} . (\frac{-1}{2}) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
2. \(\left(y^{\frac{5}{6}}\right)^{-1}\\= y^{ \frac{5}{6} . (-1) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
3. \(\left(x^{\frac{1}{3}}\right)^{-1}\\= x^{ \frac{1}{3} . (-1) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
4. \(\left(y^{\frac{-2}{3}}\right)^{1}\\= y^{ \frac{-2}{3} . 1 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
5. \(\left(a^{\frac{-5}{4}}\right)^{-1}\\= a^{ \frac{-5}{4} . (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
6. \(\left(q^{\frac{-3}{2}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-3}{2} . (\frac{-5}{4}) }= q^{\frac{15}{8}}\\=\sqrt[8]{ q^{15} }=|q|.\sqrt[8]{ q^{7} }\\---------------\)
7. \(\left(a^{1}\right)^{\frac{1}{6}}\\= a^{ 1 . \frac{1}{6} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
8. \(\left(q^{\frac{-2}{5}}\right)^{\frac{1}{5}}\\= q^{ \frac{-2}{5} . \frac{1}{5} }= q^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ q^{2} }}=\frac{1}{\sqrt[25]{ q^{2} }}. \color{purple}{\frac{\sqrt[25]{ q^{23} }}{\sqrt[25]{ q^{23} }}} \\=\frac{\sqrt[25]{ q^{23} }}{q}\\---------------\)
9. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-5}{3}}\\= x^{ \frac{-3}{4} . (\frac{-5}{3}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
10. \(\left(y^{\frac{5}{6}}\right)^{\frac{-5}{3}}\\= y^{ \frac{5}{6} . (\frac{-5}{3}) }= y^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[18]{ y^{7} }}=\frac{1}{|y|.\sqrt[18]{ y^{7} }} \color{purple}{\frac{\sqrt[18]{ y^{11} }}{\sqrt[18]{ y^{11} }}} \\=\frac{\sqrt[18]{ y^{11} }}{|y^{2}|}\\---------------\)
11. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{2} . (\frac{-1}{2}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
12. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-2}{5} . (\frac{-3}{4}) }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)