Question 12

(1/8)^2 = (0.25)^3

The expression (1/8)^2 simplifies to 1/64, which is also equal to (0.25)^3 when calculated. Therefore, option C accurately represents this equality.

A) (0.25)^2

This option evaluates to 0.0625, which is equal to 1/16. Since 1/64 is not equal to 1/16, this option is incorrect.

B) (0.5)^5

Calculating (0.5)^5 gives us 0.03125, which equals 1/32. Since this does not match 1/64, option B is also incorrect.

C) (0.25)^3

This option equals 0.015625, which is equal to 1/64. This matches the result of (1/8)^2, making option C the correct choice.

D) (0.125)^3

Evaluating (0.125)^3 results in 0.001953125, which is equal to 1/512. Since this does not equal 1/64, option D is incorrect.

E) (0.125)^4

Calculating (0.125)^4 results in 0.000244140625, which equals 1/4096. This is far from 1/64, thus making option E incorrect.

Conclusion

Option C is definitively correct because it accurately represents the value of (1/8)^2, equating to 1/64. All other options fail to provide the correct equivalence, as they either yield different values or do not relate to the original expression.