What is the value of \((0.02^3 + 0.004^3) \div (0.2^3 + 0.04^3)\)?
0.001
Notice that \(0.02 = \frac{0.2}{10}\) and \(0.004 = \frac{0.04}{10}\)
So the numerator:
\(0.02^3 + 0.004^3 = \left(\frac{0.2}{10}\right)^3 + \left(\frac{0.04}{10}\right)^3 = \frac{1}{10^3}\left(0.2^3 + 0.04^3\right)\)
Therefore:
\(\frac{0.02^3 + 0.004^3}{0.2^3 + 0.04^3} = \frac{\frac{1}{1000}(0.2^3 + 0.04^3)}{0.2^3 + 0.04^3} = \frac{1}{1000} = \mathbf{0.001}\)
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