Answered

Express the following product as a power of 2:

[tex]\[
\underbrace{2 \times 2 \times 2 \times 2 \times \ldots \ldots \times 2}_{20 \text{ factors}} = 2^{20}
\][/tex]



Answer :

To solve for [tex]\(2^{20}\)[/tex], we need to raise the number 2 to the power of 20.

Let's break down the process step by step:
1. Start with the base number, which is 2.
2. Raise it to the power of 20, which means multiplying 2 by itself 20 times.

To make it clearer, we can think of smaller powers and extend our logic from there:
- [tex]\(2^1 = 2\)[/tex]
- [tex]\(2^2 = 4\)[/tex]
- [tex]\(2^3 = 8\)[/tex]
- [tex]\(2^4 = 16\)[/tex]
... and so on.

Continuing this pattern up to [tex]\(2^{20}\)[/tex], we find:

[tex]\[ 2^{20} = 1,048,576 \][/tex]

Therefore, the value of [tex]\(2^{20}\)[/tex] is [tex]\(1,048,576\)[/tex].