The value of $\frac{(0.321)^3+(0.456)^3-(0.777)^3}{0.9 \times (0.107)(0.76)(0.777)}$ is

-6

We know that if,

 a + b + c = 0

Then, a³ + b³ + c³ = 3abc

$\frac{(0.321)^3+(0.456)^3-(0.777)^3}{0.9 \times (0.107)(0.76)(0.777)}$

0.321 + 0.456 – 0.777 = 0

Then 0.321³ + 0.456³ – 0.777³ = – 3 × 0.321 × 0.456 × 0.777

$-3 \times \frac{(0.321)\times(0.456)\times(0.777) }{0.9 \times (0.107)(0.76)(0.777)}$

$\frac{(0.321)^3+(0.456)^3-(0.777)^3}{0.9 \times (0.107)(0.76)(0.777)}$ = -6