Simplify: \(\dfrac{{(0.5)^3 + (0.05)^3 + (0.005)^3}}{{(0.1)^3 + (0.01)^3 + (0.001)^3}}\)
125
Note that \(0.5 = 5 \times 0.1,\ 0.05 = 5 \times 0.01,\ 0.005 = 5 \times 0.001\).
\(\text{{Numerator}} = (5 \times 0.1)^3 + (5 \times 0.01)^3 + (5 \times 0.001)^3 = 5^3[(0.1)^3 + (0.01)^3 + (0.001)^3]\)
\(\dfrac{{5^3 \cdot [(0.1)^3+(0.01)^3+(0.001)^3]}}{{(0.1)^3+(0.01)^3+(0.001)^3}} = 5^3 = \mathbf{{125}}\)
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