What is the simplified value of \(\dfrac{(0.25)^3 + (0.05)^3}{(0.5)^3 + (0.1)^3}\)?
0.125
Notice that 0.25 = 0.5 / 2 and 0.05 = 0.1 / 2. So the numerator is \(\dfrac{1}{2^3}\) times the denominator.
Factor out the common factor:
\((0.25)^3 + (0.05)^3 = \left(\dfrac{0.5}{2}\right)^3 + \left(\dfrac{0.1}{2}\right)^3 = \dfrac{(0.5)^3}{8} + \dfrac{(0.1)^3}{8} = \dfrac{(0.5)^3 + (0.1)^3}{8}\)
Therefore:
\(\dfrac{(0.25)^3 + (0.05)^3}{(0.5)^3 + (0.1)^3} = \dfrac{1}{8} = 0.125\)
Hence the simplified value is 0.125.
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