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Question:

Simplify the folowing expression.

$\left(\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\right)$ + $\left(\frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}\right)$ + (6 × 6 × 6) + 3$\left(\frac{1}{2}+\frac{3}{2}\right)$ $\left(\frac{1}{2}+6\right)$ $\left(6+\frac{3}{2}\right)$​​​​​​​

Explanation:

Given, $\left(\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\right)$ + $\left(\frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}\right)$ + (6 × 6 × 6) + 3$\left(\frac{1}{2}+\frac{3}{2}\right)$ $\left(\frac{1}{2}+6\right)$ $\left(6+\frac{3}{2}\right)$

= $\frac{1}{8}$ + $\frac{27}{8}$ + 216 + 6 × $\frac{13}{2}$ × $\frac{15}{2}$

= $\frac{28}{8}$ + 216 + $\frac{1170}{4}$

= $\frac{7}{2}$ + 216 + $\frac{585}{2}$

= 216 + $\frac{592}{2}$

= 216 + 296

= 512

Hence, option (c).