Sure, let's multiply the numbers given and write the answer in scientific notation.
1. Write the numbers in their full form:
[tex]\( 4 \times 10^3 = 4000 \)[/tex]
[tex]\( 5 \times 10^3 = 5000 \)[/tex]
2. Multiply the numbers:
[tex]\( 4000 \times 5000 = 20000000 \)[/tex]
3. Convert the product into scientific notation:
To express [tex]\( 20000000 \)[/tex] in scientific notation, we need to write it as a product of a number between 1 and 10 and a power of 10.
[tex]\( 20000000 = 2 \times 10^7 \)[/tex]
However, let's reflect the proper significant figures involved from the multiplication process:
[tex]\( 4 \times 5 = 20 \)[/tex] (significant part) and [tex]\( 10^3 \times 10^3 = 10^{6} \)[/tex] (exponential part).
4. Combine these results:
[tex]\( 20 \times 10^6 \)[/tex]
Another way to write this in a more simplified scientific notation could be:
[tex]\[ 2.0 \times 10^{7+1} = 2.0 \times 10^8 \][/tex]
Therefore, the result of multiplying [tex]\( (4 \times 10^3)\left(5 \times 10^3\right) \)[/tex] is [tex]\( 20 \times 10^6 \)[/tex] which can be written as [tex]\( 20e6 \)[/tex].
