Certainly! Let's go through this step-by-step:
1. Calculate [tex]\(2^{15}\)[/tex]
[tex]\[
2^{15} = 32768
\][/tex]
So, the number [tex]\(32768\)[/tex] is the result of raising [tex]\(2\)[/tex] to the power of [tex]\(15\)[/tex].
2. Find a factor of [tex]\(32768\)[/tex]
- For simplicity, let's choose the number itself as a factor. Thus, [tex]\( 32768 \)[/tex] is a factor of [tex]\( 32768 \)[/tex].
3. Divide this factor by 4 to find the quotient
[tex]\[
\text{Quotient} = \frac{32768}{4} = 8192
\][/tex]
Thus, the quotient when dividing [tex]\(32768\)[/tex] (which is a factor of [tex]\(2^{15}\)[/tex]) by 4 is [tex]\(8192\)[/tex].
Therefore, among the multiple-choice options provided, none of them (22, 32, 42, or 52) is correct when considering the calculation. The correct quotient is [tex]\(8192\)[/tex].
It seems there may be an error or missing information in the multiple-choice answers provided, but the correct numerical result for the division is [tex]\(8192\)[/tex].
