The value of $$\left( {\frac{{0.125 + 0.027}}{{0.5 \times 0.5 + 0.09 - 0.15}}} \right)$$     is :

Solution(By Examveda Team)

Given expression :
$$\eqalign{ & \frac{{0.125 + 0.027}}{{0.5 \times 0.5 + 0.09 - 0.15}} \cr & = \frac{{{{\left( {0.5} \right)}^3} + {{\left( {0.3} \right)}^3}}}{{{{\left( {0.5} \right)}^2} + {{\left( {0.3} \right)}^2} - \left( {0.5 \times 0.3} \right)}} \cr & = \left( {\frac{{{a^3} + {b^3}}}{{{a^2} + {b^2} - ab}}} \right) \cr & = \frac{{\left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}}{{\left( {{a^2} - ab + {b^2}} \right)}} \cr & = (a + b) \cr & = \left( {0.5 + 0.3} \right) \cr & = 0.8 \cr} $$