To write the expression [tex]\(12^{-2}\)[/tex] in simplest form, we need to understand what the negative exponent indicates. A negative exponent means we're dealing with the reciprocal of the base raised to the positive of that exponent. Here are the steps:
1. Identify the base and the exponent: In the expression [tex]\(12^{-2}\)[/tex], the base is 12 and the exponent is -2.
2. Rewrite the expression using the reciprocal: A negative exponent [tex]\(-n\)[/tex] means [tex]\(\frac{1}{(\text{base})^n}\)[/tex]. Thus, [tex]\(12^{-2} = \frac{1}{12^2}\)[/tex].
3. Calculate the power of 12: [tex]\(12^2\)[/tex] means 12 raised to the power of 2, which is [tex]\(12 \times 12 = 144\)[/tex].
4. Form the reciprocal: Now we take the reciprocal of 144. So, [tex]\(\frac{1}{144}\)[/tex] is the simplest form.
When we convert the fraction [tex]\(\frac{1}{144}\)[/tex] to a decimal, we get approximately 0.006944444444444444. For practical purposes and an approximation, we can round this to four decimal places, which gives us 0.0069.
Therefore, the expression [tex]\(12^{-2}\)[/tex] in simplest form is:
[tex]\[
\frac{1}{144}
\][/tex]
And if we convert and round it off to four decimal places:
[tex]\[
0.0069
\][/tex]
