Question 8

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

Calculating (1/25)^3 results in (0.04)^3, as both expressions represent the same numerical value when simplified.

A) (0.008)^3

This option is incorrect because (0.008)^3 equals 0.000512, which does not match the value of (1/25)^3. The cube of 0.008 is significantly smaller than the cube of 0.04.

B) (0.04)^3

This option is correct because (1/25) is equivalent to 0.04, and thus (1/25)^3 simplifies directly to (0.04)^3, which accurately represents the same value.

C) (0.2)^3

This option is incorrect as (0.2)^3 equals 0.008, which is not equal to (1/25)^3. The cube of 0.2 is too large when compared to the value of (1/25)^3.

D) (0.2)^5

This option is also incorrect because (0.2)^5 equals 0.00032, which again does not match the value of (1/25)^3. The exponent and base combination results in a much smaller number.

E) (0.25)^3

This option is incorrect since (0.25)^3 equals 0.015625, which is not equal to (1/25)^3. The value produced by cubing 0.25 is greater than the value of (1/25)^3.

Conclusion

Option B is definitively correct as it accurately represents the simplified form of (1/25)^3. All other options either result in values that are significantly larger or smaller than the correct answer, demonstrating their incorrectness in relation to the original expression.