Simplify 3 \sqrt[3]{a} - \sqrt[5] {a}^(2) * ( {a}^( - 1) )^ (1)/(2) ​

Question

Simplify 3


`\sqrt[3]{a} - \sqrt[5] {a}^(2) * ( {a}^( - 1) )^ (1)/(2)`
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Answer 1

why is there no picture?

Answer 2

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Answer:

cuberoot(a) - 1/tenthroot(a)

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 ...

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

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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.