To solve the expression [tex]\(2 \times 10^2 \times 2 \times 10^3\)[/tex], we will follow a step-by-step approach:
### Step 1: Multiply the constants
First, multiply the numeric coefficients:
[tex]\[ 2 \times 2 = 4 \][/tex]
### Step 2: Combine the powers of 10
Next, use the properties of exponents to combine the powers of 10. Specifically, when multiplying like bases, you add the exponents:
[tex]\[ 10^2 \times 10^3 = 10^{2+3} = 10^5 \][/tex]
### Step 3: Combine the results
Now, combine the product of the numeric coefficients with the combined power of 10:
[tex]\[ 4 \times 10^5 \][/tex]
So, the solution to [tex]\(2 \times 10^2 \times 2 \times 10^3\)[/tex] is [tex]\(4 \times 10^5\)[/tex].
### Final Answer
The answer in scientific notation is:
[tex]\[ 4 \times 10^5 \][/tex]
This is equal to 400,000.0.
