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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)
2. \(\left(y^{1}\right)^{\frac{-2}{3}}\\= y^{ 1 . (\frac{-2}{3}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
3. \(\left(x^{2}\right)^{\frac{-1}{6}}\\= x^{ 2 . (\frac{-1}{6}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
4. \(\left(y^{\frac{-1}{6}}\right)^{\frac{1}{6}}\\= y^{ \frac{-1}{6} . \frac{1}{6} }= y^{\frac{-1}{36}}\\=\frac{1}{\sqrt[36]{ y }}=\frac{1}{\sqrt[36]{ y }}. \color{purple}{\frac{\sqrt[36]{ y^{35} }}{\sqrt[36]{ y^{35} }}} \\=\frac{\sqrt[36]{ y^{35} }}{|y|}\\---------------\)
5. \(\left(y^{\frac{3}{2}}\right)^{\frac{-5}{4}}\\= y^{ \frac{3}{2} . (\frac{-5}{4}) }= y^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ y^{15} }}\\=\frac{1}{|y|.\sqrt[8]{ y^{7} }}=\frac{1}{|y|.\sqrt[8]{ y^{7} }} \color{purple}{\frac{\sqrt[8]{ y }}{\sqrt[8]{ y }}} \\=\frac{\sqrt[8]{ y }}{|y^{2}|}\\---------------\)
6. \(\left(a^{\frac{-1}{6}}\right)^{\frac{5}{2}}\\= a^{ \frac{-1}{6} . \frac{5}{2} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
7. \(\left(x^{\frac{3}{4}}\right)^{\frac{-2}{3}}\\= x^{ \frac{3}{4} . (\frac{-2}{3}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-3}{5} . (\frac{-3}{5}) }= a^{\frac{9}{25}}\\=\sqrt[25]{ a^{9} }\\---------------\)
9. \(\left(x^{\frac{-3}{5}}\right)^{-1}\\= x^{ \frac{-3}{5} . (-1) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
10. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-1}{2} . (\frac{-5}{6}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
11. \(\left(q^{-1}\right)^{-1}\\= q^{ -1 . (-1) }= q^{1}\\\\---------------\)
12. \(\left(y^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{2} . \frac{2}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)