(1/25)^3 =

Rationale

(1/25)^3 = (0.04)^3.

To evaluate ((1/25)^3), we first simplify ((1/25)) to its decimal form, which is (0.04). Therefore, raising (0.04) to the power of 3 gives us an equivalent expression.

A ((0.008)^3) YOUR ANSWER

Calculating ((0.008)^3) results in (0.000512), which does not equal ((1/25)^3) or ((0.04)^3). Thus, this option is incorrect as it represents a different decimal value.

B ((0.04)^3) CORRECT

This expression is indeed equivalent to ((1/25)^3). When we calculate ((0.04)^3), we find that it equals (0.000064), which matches the value we derive from ((1/25)^3), confirming it as the correct choice.

C ((0.2)^3) YOUR ANSWER

Calculating ((0.2)^3) yields (0.008). This value is significantly larger than ((1/25)^3) and therefore cannot be correct. The decimal (0.2) does not relate to (0.04) in magnitude.

D ((0.2)^5) YOUR ANSWER

This expression results in (0.00032). While it is a small number, it still does not equal ((1/25)^3) or ((0.04)^3). The exponentiation of (0.2) to the fifth power leads to a different value entirely.

E ((0.25)^3) YOUR ANSWER

Calculating ((0.25)^3) yields (0.015625). This value is much larger than ((1/25)^3) and therefore is not a correct equivalence, further confirming that it cannot be the answer.

Conclusion

The expression ((1/25)^3) simplifies to ((0.04)^3), making option B the only correct choice. All other options provide results that differ from this expression, either because they represent different decimal values or incorrect powers. Understanding the proper conversion between fractions and decimals is essential for solving such problems accurately.

(1/25)^3 =

(1/25)^3 = (0.04)^3.

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