To determine which expression is equivalent to [tex]\((2.0 \times 10^3)(2.0 \times 10^4)\)[/tex], let's break the problem into smaller, more manageable steps.
1. Separate and Multiply the Bases:
The expression has the form [tex]\((a \times 10^m)(b \times 10^n)\)[/tex], where [tex]\(a = 2.0\)[/tex], [tex]\(m = 3\)[/tex], [tex]\(b = 2.0\)[/tex], and [tex]\(n = 4\)[/tex].
First, we multiply the bases (the numbers outside of the powers of 10):
[tex]\[
2.0 \times 2.0 = 4.0
\][/tex]
2. Add the Exponents:
Next, we add the exponents from the powers of 10:
[tex]\[
10^3 \times 10^4 = 10^{3+4} = 10^7
\][/tex]
3. Combine the Results:
Now, we put together the results from the previous steps:
[tex]\[
(2.0 \times 10^3) \times (2.0 \times 10^4) = 4.0 \times 10^7
\][/tex]
Therefore, [tex]\((2.0 \times 10^3)(2.0 \times 10^4)\)[/tex] is equivalent to [tex]\(4.0 \times 10^7\)[/tex].
So, the correct answer is
[tex]\[
\boxed{4.0 \times 10^7}
\][/tex]
