(1/8)^2 =

Rationale

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

To solve the equation, we first convert ( \frac{1}{8} ) to its decimal form, which is 0.125. Thus, squaring ( 0.125 ) gives us ( 0.125^2 = 0.015625 ). On the other hand, ( (0.25)^3 ) calculates to ( 0.25 × 0.25 × 0.25 = 0.015625 ), confirming that they are equal.

A ((0.25)^2) YOUR ANSWER

Calculating ( (0.25)^2 ) results in ( 0.0625 ), which is not equal to ( (1/8)^2 ). This choice represents a different power and thus does not satisfy the equation.

B ((0.5)^5) YOUR ANSWER

Calculating ( (0.5)^5 ) gives ( 0.5 × 0.5 × 0.5 × 0.5 × 0.5 = 0.03125 ). This value is also not equivalent to ( (1/8)^2 ), making it an incorrect choice.

D ((0.125)^3) YOUR ANSWER

Calculating ( (0.125)^3 ) yields ( 0.125 × 0.125 × 0.125 = 0.001953125 ). Since this value is far smaller than ( (1/8)^2 ), it does not match and is therefore incorrect.

E ((0.125)^4) YOUR ANSWER

Calculating ( (0.125)^4 ) results in ( 0.125 × 0.125 × 0.125 × 0.125 = 0.000244140625 ). This value is significantly lower than ( (1/8)^2 ), confirming that this choice is incorrect.

Conclusion

The expression ( (1/8)^2 ) simplifies to ( 0.015625 ), which is identical to ( (0.25)^3 ). The other options, while they involve powers of similar decimals, do not equate to this value, confirming that ( (0.25)^3 ) is the only correct answer.

(1/8)^2 =

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

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