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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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