Answer :
To solve the expression [tex]\(4^{-2}\)[/tex], let's understand what negative exponents represent. A negative exponent indicates that the base should be taken as the reciprocal and then raised to the given positive power.
Here are the steps to evaluate [tex]\(4^{-2}\)[/tex]:
1. Identify the base and the exponent:
- The base here is 4.
- The exponent is -2.
2. Apply the rule for negative exponents:
- According to the rule, [tex]\(a^{-n} = \frac{1}{a^n}\)[/tex]. This means that the negative exponent turns the base into the reciprocal, raised to the positive of that exponent.
3. Compute [tex]\(4^{-2}\)[/tex]:
- Convert [tex]\(4^{-2}\)[/tex] to [tex]\(\frac{1}{4^2}\)[/tex].
4. Square the base:
- Calculate [tex]\(4^2\)[/tex]:
[tex]\[
4^2 = 4 \times 4 = 16
\][/tex]
5. Take the reciprocal:
- Now, replace [tex]\(4^2\)[/tex] in the expression:
[tex]\[
\frac{1}{4^2} = \frac{1}{16}
\][/tex]
After evaluating the expression, we find that [tex]\(4^{-2}\)[/tex] is equivalent to [tex]\(\frac{1}{16}\)[/tex].
Therefore, the correct choice matching this result is A. [tex]\(\frac{1}{16}\)[/tex].
Here are the steps to evaluate [tex]\(4^{-2}\)[/tex]:
1. Identify the base and the exponent:
- The base here is 4.
- The exponent is -2.
2. Apply the rule for negative exponents:
- According to the rule, [tex]\(a^{-n} = \frac{1}{a^n}\)[/tex]. This means that the negative exponent turns the base into the reciprocal, raised to the positive of that exponent.
3. Compute [tex]\(4^{-2}\)[/tex]:
- Convert [tex]\(4^{-2}\)[/tex] to [tex]\(\frac{1}{4^2}\)[/tex].
4. Square the base:
- Calculate [tex]\(4^2\)[/tex]:
[tex]\[
4^2 = 4 \times 4 = 16
\][/tex]
5. Take the reciprocal:
- Now, replace [tex]\(4^2\)[/tex] in the expression:
[tex]\[
\frac{1}{4^2} = \frac{1}{16}
\][/tex]
After evaluating the expression, we find that [tex]\(4^{-2}\)[/tex] is equivalent to [tex]\(\frac{1}{16}\)[/tex].
Therefore, the correct choice matching this result is A. [tex]\(\frac{1}{16}\)[/tex].