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

QUESTION

The value of $\dpi{120} \fn_jvn \large 3\sqrt{\frac{-a^6 \times b^3 \times c^2^1}{c^9 \times a^1^2}}$ is ______ .

 OPTIONS A. $\dpi{120} \fn_jvn \large \frac{-bc^3}{a^2}$ B. $\dpi{120} \fn_jvn \large \frac{bc^4}{a^2}$ C. $\dpi{120} \fn_jvn \large \frac{-ab^4}{c^2}$ D. $\dpi{120} \fn_jvn \large \frac{-bc^4}{a^2}$
Right Option : D

EXPLANATION
Explain TypeExplanation Content
Text

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

$=\left ( \frac{(-b)\times (-b)\times (-b)\times c^4 \times c^4 \times c^4}{a^2\times a^2\times a^2} \right )^\frac{^1}{^3}=\left ( \frac{-b\times c^4}{a^2} \right )^3^X\frac{^1}{^3}=\frac{-bc^4}{a^2}$

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