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simplify 3
[tex] \sqrt[3]{a} - \sqrt[5] {a}^{2} \times ( {a}^{ - 1} )^ \frac{1}{2} [/tex]
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Sagot :

johnpatrickanat

Answer:

why is there no picture?

sqdancefan

9514 1404 393

Answer:

  cuberoot(a) - 1/tenthroot(a)

Step-by-step explanation:

The applicable rule of exponents seems to be ...

  (a^b)^c = a^(bc)

  a^-b = 1/a^b

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Expressing all radicals using rational exponents, we want to simplify ...

  [tex]a^{\frac{1}{3}}-(a^{\frac{2}{5}})(a^{-\frac{1}{2}})\\\\=a^{\frac{1}{3}}-a^{\frac{4-5}{10}}\\\\=a^{\frac{1}{3}}-a^{-\frac{1}{10}}=\boxed{\sqrt[3]{a}-\dfrac{1}{\sqrt[10]{a}}}\\\\=\boxed{\sqrt[3]{a}-\dfrac{\sqrt[10]{a^9}}{a}}[/tex]

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We have shown two simplified expressions. You can choose the one that matches your requirements. Sometimes we don't want any radicals in the denominator.

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