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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{4}}\right)^{\frac{-4}{5}}\\= a^{ \frac{5}{4} . (\frac{-4}{5}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
2. \(\left(x^{2}\right)^{\frac{-1}{2}}\\= x^{ 2 . (\frac{-1}{2}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
3. \(\left(y^{1}\right)^{-2}\\= y^{ 1 . (-2) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
4. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{4} . (\frac{-1}{2}) }= y^{\frac{1}{8}}\\=\sqrt[8]{ y }\\---------------\)
5. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{2}{3} . (\frac{-1}{6}) }= a^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ a }}=\frac{1}{\sqrt[9]{ a }}. \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a}\\---------------\)
6. \(\left(y^{-2}\right)^{1}\\= y^{ -2 . 1 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
7. \(\left(q^{1}\right)^{\frac{-1}{3}}\\= q^{ 1 . (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
8. \(\left(y^{\frac{-1}{6}}\right)^{1}\\= y^{ \frac{-1}{6} . 1 }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
9. \(\left(x^{\frac{2}{5}}\right)^{\frac{-4}{5}}\\= x^{ \frac{2}{5} . (\frac{-4}{5}) }= x^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ x^{8} }}=\frac{1}{\sqrt[25]{ x^{8} }}. \color{purple}{\frac{\sqrt[25]{ x^{17} }}{\sqrt[25]{ x^{17} }}} \\=\frac{\sqrt[25]{ x^{17} }}{x}\\---------------\)
10. \(\left(q^{-1}\right)^{\frac{-5}{6}}\\= q^{ -1 . (\frac{-5}{6}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
11. \(\left(a^{\frac{-1}{2}}\right)^{-2}\\= a^{ \frac{-1}{2} . (-2) }= a^{1}\\\\---------------\)
12. \(\left(x^{\frac{3}{2}}\right)^{1}\\= x^{ \frac{3}{2} . 1 }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)