Explain why $$ -2^{-2}=-\frac{1}{4} $$, but $$ (-2)^{-2}=\frac{1}{4} $$. Choose the correct answer below. A. In the first equation, the exponent is applied to the base 2 , while in the second equation, the exponent is applied to the base -2 . B. The negative of an exponential expression is always negative, but raising a negative base to a power will always result in a positive number. C. Because the base in the second equation is -2 , the negative sign in the exponent is distributed to the base. D. If the base of an exponential expression is in parentheses, it will always be positive after applying the exponent.

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The given equations are:

1. $$ -2^{-2} = -\frac{1}{4} $$
2. $$ (-2)^{-2} = \frac{1}{4} $$

Let's analyze each equation:

1. In the first equation, the negative sign is applied to the base 2, which results in a negative value. The exponent -2 is then applied to this negative base, resulting in $$ -2^{-2} = -\frac{1}{4} $$.

2. In the second equation, the base is -2, which is already negative. When the exponent -2 is applied to this negative base, the negative sign in the exponent is distributed to the base, resulting in $$ (-2)^{-2} = \frac{1}{4} $$.

Therefore, the correct explanation is:

C. Because the base in the second equation is -2, the negative sign in the exponent is distributed to the base.
The correct answer is C: Because the base in the second equation is -2, the negative sign in the exponent is distributed to the base.

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