Let's determine which of the provided answers shows the number [tex]\(2.13786 \times 10^4\)[/tex] written in standard form.
We need to multiply [tex]\(2.13786\)[/tex] by [tex]\(10^4\)[/tex].
[tex]\(10^4\)[/tex] means [tex]\(10\)[/tex] raised to the 4th power, which is equal to 10,000.
So we have:
[tex]\[2.13786 \times 10,000\][/tex]
When multiplying a number by [tex]\(10,000\)[/tex], you effectively move the decimal point 4 places to the right.
Starting with [tex]\(2.13786\)[/tex]:
1. Move the decimal point one place to the right: [tex]\(21.3786\)[/tex]
2. Move the decimal point another place to the right: [tex]\(213.786\)[/tex]
3. Move the decimal point another place to the right: [tex]\(2137.86\)[/tex]
4. Move the decimal point another place to the right: [tex]\(21378.6\)[/tex]
So, the number [tex]\(2.13786 \times 10^4\)[/tex] written in standard form is:
[tex]\[21,378.6\][/tex]
Therefore, the answer is [tex]\(\boxed{21,378.6}\)[/tex].
