Answer :
To solve the expression [tex]\( 4^{-2} \)[/tex], we need to understand what the negative exponent indicates. A negative exponent means we take the reciprocal of the base raised to the positive of that exponent. Here’s a step-by-step breakdown:
1. The expression given is [tex]\( 4^{-2} \)[/tex].
2. A negative exponent means you take the reciprocal. So, [tex]\( 4^{-2} \)[/tex] becomes [tex]\( \frac{1}{4^2} \)[/tex].
3. Next, calculate [tex]\( 4^2 \)[/tex], which is [tex]\( 4 \times 4 = 16 \)[/tex].
4. Therefore, [tex]\( \frac{1}{4^2} \)[/tex] becomes [tex]\( \frac{1}{16} \)[/tex].
The expression [tex]\( 4^{-2} \)[/tex] is equivalent to [tex]\( \frac{1}{16} \)[/tex].
Thus, the correct choice is D. [tex]\(\frac{1}{16}\)[/tex].
1. The expression given is [tex]\( 4^{-2} \)[/tex].
2. A negative exponent means you take the reciprocal. So, [tex]\( 4^{-2} \)[/tex] becomes [tex]\( \frac{1}{4^2} \)[/tex].
3. Next, calculate [tex]\( 4^2 \)[/tex], which is [tex]\( 4 \times 4 = 16 \)[/tex].
4. Therefore, [tex]\( \frac{1}{4^2} \)[/tex] becomes [tex]\( \frac{1}{16} \)[/tex].
The expression [tex]\( 4^{-2} \)[/tex] is equivalent to [tex]\( \frac{1}{16} \)[/tex].
Thus, the correct choice is D. [tex]\(\frac{1}{16}\)[/tex].