To find the value of [tex]\(a\)[/tex] in the table, we need to look at the pattern of values for different negative powers of 2.
Let's summarize the given values from the table first:
- [tex]\(2^{-1} = \frac{1}{2}\)[/tex]
- [tex]\(2^{-2} = \frac{1}{4}\)[/tex]
- [tex]\(2^{-3} = \frac{1}{8}\)[/tex]
- [tex]\(2^{-4} = \frac{1}{16}\)[/tex]
- [tex]\(2^{-5} = \frac{1}{32}\)[/tex]
Notice that these values follow a specific pattern. Each time the exponent decreases by 1, the value is halved. For example:
- [tex]\(\frac{1}{2}\)[/tex] divided by 2 is [tex]\(\frac{1}{4}\)[/tex]
- [tex]\(\frac{1}{4}\)[/tex] divided by 2 is [tex]\(\frac{1}{8}\)[/tex]
- [tex]\(\frac{1}{8}\)[/tex] divided by 2 is [tex]\(\frac{1}{16}\)[/tex]
- [tex]\(\frac{1}{16}\)[/tex] divided by 2 is [tex]\(\frac{1}{32}\)[/tex]
Based on this pattern, the next value in the sequence for [tex]\(2^{-6}\)[/tex] should also be [tex]\(\frac{1}{32}\)[/tex] divided by 2:
- [tex]\(\frac{1}{32} \div 2 = \frac{1}{64}\)[/tex]
When expressed as a decimal, [tex]\(\frac{1}{64} = 0.015625\)[/tex]. Therefore, the value of [tex]\(a\)[/tex], which is [tex]\(2^{-6}\)[/tex], is [tex]\(0.015625\)[/tex].
