What is the Value of $\frac{0.74 \times 1.23 \times 0.13}{(0.37)^3 + (0.41)^3 - 8(0.39)^3}$?

$\frac{-1}{3}$

$\frac{0.74 \times 1.23 \times 0.13}{(0.37)^3 + (0.41)^3 - 8(0.39)^3}$

= $\frac{0.74 \times 1.23 \times 0.13}{(0.37)^3 + (0.41)^3 - (0.78)^3}$

If a + b + c = 0, then a³ + b³ + c³ = 3abc

So, 0.37 + 0.41 – 0.78 = 0, then 0.37³ + 0.41³ – 0.78³ = – 3 × 0.37 × 0.41 × 0.78

= $\frac{0.74 \times 1.23 \times 0.13}{– 3 × 0.37 × 0.41 × 0.78}$

= \(\frac{-1}{3}\)