The value of $$\frac{{\left( {0.545} \right)\left( {0.081} \right)\left( {0.51} \right)\left( {5.2} \right)}}{{{{\left( {0.324} \right)}^3} + {{\left( {0.221} \right)}^3} - {{\left( {0.545} \right)}^3}}}{\text{is:}}$$

Solution (By Examveda Team)

$$\eqalign{ & {a^3} + {b^3} + {c^3} = 3abc \cr & {\text{If }}a + b + c = 0 \cr & a = 0.324 \cr & b = 0.221 \cr & c = - 0.545 \cr & \frac{{\left( {0.545} \right)\left( {0.081} \right)\left( {0.51} \right)\left( {5.2} \right)}}{{3abc}} \cr & = - \frac{{0.545 \times 0.081 \times 0.51 \times 5.2}}{{3 \times 0.324 \times 0.221 \times 0.545}} \cr & = - \frac{{81 \times 510 \times 5.2}}{{3 \times 18 \times 18 \times 13 \times 17}} \cr & = - 1 \cr} $$