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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{2}}\right)^{-1}\\= x^{ \frac{-1}{2} . (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
2. \(\left(x^{\frac{5}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{5}{2} . \frac{1}{2} }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-1}{3} . (\frac{-1}{3}) }= a^{\frac{1}{9}}\\=\sqrt[9]{ a }\\---------------\)
4. \(\left(y^{\frac{-3}{2}}\right)^{\frac{4}{5}}\\= y^{ \frac{-3}{2} . \frac{4}{5} }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
5. \(\left(a^{\frac{-1}{5}}\right)^{\frac{4}{5}}\\= a^{ \frac{-1}{5} . \frac{4}{5} }= a^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ a^{4} }}=\frac{1}{\sqrt[25]{ a^{4} }}. \color{purple}{\frac{\sqrt[25]{ a^{21} }}{\sqrt[25]{ a^{21} }}} \\=\frac{\sqrt[25]{ a^{21} }}{a}\\---------------\)
6. \(\left(y^{\frac{2}{5}}\right)^{\frac{-5}{3}}\\= y^{ \frac{2}{5} . (\frac{-5}{3}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
7. \(\left(q^{1}\right)^{\frac{-1}{5}}\\= q^{ 1 . (\frac{-1}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
8. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{3} . (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
9. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-1}{6} . (\frac{-2}{3}) }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)
10. \(\left(x^{-1}\right)^{\frac{5}{2}}\\= x^{ -1 . \frac{5}{2} }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
11. \(\left(y^{\frac{1}{6}}\right)^{1}\\= y^{ \frac{1}{6} . 1 }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
12. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-4}{3}}\\= q^{ \frac{-2}{3} . (\frac{-4}{3}) }= q^{\frac{8}{9}}\\=\sqrt[9]{ q^{8} }\\---------------\)