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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{2}}\right)^{-1}\\= x^{ \frac{5}{2} . (-1) }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
2. \(\left(y^{\frac{1}{4}}\right)^{\frac{-3}{5}}\\= y^{ \frac{1}{4} . (\frac{-3}{5}) }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{3} . (\frac{-1}{2}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
4. \(\left(x^{\frac{-1}{5}}\right)^{\frac{2}{5}}\\= x^{ \frac{-1}{5} . \frac{2}{5} }= x^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ x^{2} }}=\frac{1}{\sqrt[25]{ x^{2} }}. \color{purple}{\frac{\sqrt[25]{ x^{23} }}{\sqrt[25]{ x^{23} }}} \\=\frac{\sqrt[25]{ x^{23} }}{x}\\---------------\)
5. \(\left(y^{\frac{4}{3}}\right)^{-2}\\= y^{ \frac{4}{3} . (-2) }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
6. \(\left(y^{\frac{1}{5}}\right)^{1}\\= y^{ \frac{1}{5} . 1 }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
7. \(\left(x^{-1}\right)^{\frac{4}{5}}\\= x^{ -1 . \frac{4}{5} }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
8. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-1}{3} . (\frac{-2}{3}) }= x^{\frac{2}{9}}\\=\sqrt[9]{ x^{2} }\\---------------\)
9. \(\left(q^{-2}\right)^{\frac{-1}{2}}\\= q^{ -2 . (\frac{-1}{2}) }= q^{1}\\\\---------------\)
10. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{2} . (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
11. \(\left(q^{\frac{-3}{5}}\right)^{\frac{1}{6}}\\= q^{ \frac{-3}{5} . \frac{1}{6} }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
12. \(\left(y^{\frac{-1}{2}}\right)^{1}\\= y^{ \frac{-1}{2} . 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)