To solve the expression [tex]\(\underbrace{2 \times 2 \times 2 \times 2 \times \ldots \times 2}_{20 \text{ factors}}\)[/tex], we recognize that we have the number 2 multiplied by itself 20 times. This can be represented using exponential notation as [tex]\(2^{20}\)[/tex].
Exponential notation [tex]\(a^b\)[/tex] means multiplying the base [tex]\(a\)[/tex] by itself [tex]\(b\)[/tex] times. For this particular example:
[tex]\[
2^{20} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2
\][/tex]
Now, let's calculate [tex]\(2^{20}\)[/tex]:
[tex]\[
2^{20} = 1,048,576
\][/tex]
So the value of the expression [tex]\(\underbrace{2 \times 2 \times 2 \times 2 \times \ldots \times 2}_{20 \text{ factors}}\)[/tex] or [tex]\(2^{20}\)[/tex] is [tex]\(1,048,576\)[/tex].
