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.
