Find the value of the following expression:
​$$\frac{(0.22 \times 0.22 \times 0.22) + (0.022 \times 0.022 \times 0.022)}{(0.66 \times 0.66 \times 0.66) + (0.066 \times 0.066 \times 0.066)}$$​​

Correct option is C

Given: 
​$$\frac{(0.22 \times 0.22 \times 0.22) + (0.022 \times 0.022 \times 0.022)}{(0.66 \times 0.66 \times 0.66) + (0.066 \times 0.066 \times 0.066)}$$ 
Solution:
$$\frac{(0.22 \times 0.22 \times 0.22) + (0.022 \times 0.022 \times 0.022)}{(0.66 \times 0.66 \times 0.66) + (0.066 \times 0.066 \times 0.066)} \\\ \\= \frac{0.22^3 + 0.022^3}{0.66^3 + 0.066^3} \\\ \\= \frac{0.22^3 (1 + 0.1^3)}{0.66^3 (1 + 0.1^3)}\\\ \\= \frac{0.22^3}{0.66^3}\\\ \\ = \left( \frac{1}{3} \right)^3 \\\ \\ = \frac 1{27}$$​​