Find the value of the expression $$\frac{0.125 + 0.027}{0.5 imes 0.5 + 0.09 - 0.15}$$.

Question

Find the value of the expression $$\frac{0.125 + 0.027}{0.5 	imes 0.5 + 0.09 - 0.15}$$.

Accepted Answer

To simplify the given expression:

1. **Numerator Calculation**:  
   $$0.125 + 0.027 = (0.5)^3 + (0.3)^3$$.

2. **Denominator Calculation**:  
   $$0.5 	imes 0.5 + 0.09 - 0.15 = (0.5)^2 + (0.3)^2 - (0.5 	imes 0.3)$$.

3. **Expression Simplification**:  
   The numerator becomes $$a^3 + b^3$$, and the denominator becomes $$a^2 + b^2 - ab$$. Using the identity $$\frac{a^3 + b^3}{a^2 + b^2 - ab} = a + b$$:  
   Substituting $$a = 0.5$$ and $$b = 0.3$$, we get:  
   $$a + b = 0.5 + 0.3 = 0.8$$.

Thus, the value of the expression is **0.8**.

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