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What exponent would make this statement true? 1/4 = 4^?

A. -1
B. -2
C. 1/4
D. 2

User Foxfire
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1 Answer

3 votes

Final answer:

To make the statement 1/4 = 4^? true, the exponent must be -2, as a base with a negative exponent represents the reciprocal of the base raised to the absolute value of the exponent.

Step-by-step explanation:

The exponent that would make the statement 1/4 = 4^? true is -2. To find this, we need to understand that a negative exponent indicates that the base (in this case, 4) should be taken as the reciprocal raised to the absolute value of the exponent. Hence, 4 raised to the power of -2 would be the same as 1 divided by 4 squared (1/4^2), which equals 1/16. However, since we want the result to be 1/4, we adjust this to 4^-1, which equals 1/4. The answer is B. -2.

User Ellis Whitehead
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