To simplify the expression [tex]\((16)^{-2}\)[/tex], follow these steps:
1. Understand the meaning of negative exponents:
A negative exponent means that the base is on the wrong side of the fraction line, so you invert the base. Specifically, [tex]\(a^{-n} = \frac{1}{a^n}\)[/tex].
2. Apply this to our expression:
Given [tex]\((16)^{-2}\)[/tex], we apply the rule for negative exponents:
[tex]\[
(16)^{-2} = \frac{1}{(16)^2}
\][/tex]
3. Calculate the positive exponent:
Next, we need to find the value of [tex]\((16)^2\)[/tex]. Multiplying 16 by itself:
[tex]\[
16 \times 16 = 256
\][/tex]
4. Formulate the fraction:
Now substitute this value back into the expression:
[tex]\[
(16)^{-2} = \frac{1}{256}
\][/tex]
5. Express the fraction as a decimal:
When you convert [tex]\(\frac{1}{256}\)[/tex] into a decimal, you get:
[tex]\[
\frac{1}{256} = 0.00390625
\][/tex]
So, [tex]\((16)^{-2} = 0.00390625\)[/tex].
Thus, the simplified value of [tex]\((16)^{-2}\)[/tex] is [tex]\(\boxed{0.00390625}\)[/tex].
