Maths / Cube and Cube Roots / Cube Root by Prime Factorisation

QUESTION
 

The value of large 3sqrt{frac{-a^6 times b^3 times c^2^1}{c^9 times a^1^2}} is ______ .

OPTIONS
A. 

large frac{-bc^3}{a^2}

B. 

large frac{bc^4}{a^2}

C. 

large frac{-ab^4}{c^2}

D. 

large frac{-bc^4}{a^2}

Right Option : D

EXPLANATION
Explain TypeExplanation Content
Text

We have, 3sqrt{frac{-a^6 times b^3 times c^2^1}{c^9 times a^1^2}}=3sqrt{frac{-b^3 times c^1^2}{a^6}}

=left ( frac{(-b)times (-b)times (-b)times c^4 times c^4 times c^4}{a^2times a^2times a^2} right )^frac{^1}{^3}=left ( frac{-btimes c^4}{a^2} right )^3^Xfrac{^1}{^3}=frac{-bc^4}{a^2}

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