Find the value of the cube root of the following fraction: That is, find the…

Concept: The cube root distributes over a quotient — ∛(a/b) = ∛a / ∛b. A terminating decimal is a perfect cube only when its number of decimal places is a multiple of 3 (so the power of 10 is itself a perfect cube) and the integer formed by its digits is a perfect cube. Writing each decimal as that integer over a power of 10 then makes the cube root easy to read off.

Application: take the cube root of the numerator and the denominator separately.

1. Numerator: 0.003375 = (0.15)3, since 153 = 3375 and shifting the decimal gives 0.003375. Hence ∛0.003375 = 0.15.

2. Denominator: 0.004913 = (0.17)3, since 173 = 4913. Hence ∛0.004913 = 0.17.

3. Combine: ∛(0.003375 / 0.004913) = 0.15 / 0.17.

4. Clear the decimals by multiplying numerator and denominator by 100: 0.15 / 0.17 = 15 / 17.

Cross-check: cube 15/17 back — (15/17)3 = 3375 / 4913 = 0.003375 / 0.004913, which matches the original fraction. So the value is 15/17.