Discussion

What is the value of \(\frac{0.1 \times 0.1 \times 0.1 + 0.02 \times 0.02 \times 0.02}{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}\)?

Answer: A

Let a = 0.1 and b = 0.02. The numerator is \(a^3 + b^3\).

The denominator can be written in terms of a and b. \(0.2 = 2 \times 0.1 = 2a\) and \(0.04 = 2 \times 0.02 = 2b\).

The denominator is \((2a)^3 + (2b)^3 = 8a^3 + 8b^3 = 8(a^3+b^3)\).

The expression is \(\frac{a^3+b^3}{8(a^3+b^3)} = \frac{1}{8}\).

\(\frac{1}{8} = 0.125\).

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