Sure, let's work through this problem step-by-step.
### Part (b)
We need to evaluate [tex]\(\left(7 \times 10^5\right) \div \left(2 \times 10^2\right)\)[/tex] and give the answer in standard form.
1. Write the expression:
[tex]\[
\frac{7 \times 10^5}{2 \times 10^2}
\][/tex]
2. Rewrite the division of the coefficients and the powers of 10 separately:
[tex]\[
\left(\frac{7}{2}\right) \times \left(\frac{10^5}{10^2}\right)
\][/tex]
3. Divide the coefficients:
[tex]\[
\frac{7}{2} = 3.5
\][/tex]
4. Simplify the powers of 10 using the properties of exponents:
[tex]\[
10^5 \div 10^2 = 10^{5-2} = 10^3
\][/tex]
5. Combine the results:
[tex]\[
3.5 \times 10^3
\][/tex]
The result in standard form is:
[tex]\[
3.5 \times 10^3
\][/tex]
In numeric form, this would be:
[tex]\[
3500
\][/tex]
So the answer to the given problem [tex]\(\left(7 \times 10^5\right) \div \left(2 \times 10^2\right)\)[/tex] is [tex]\(\mathbf{3.5 \times 10^3}\)[/tex].
### Part (a)
You asked to "Give your answer in standard form."
The result already provided in the context of part (b) fits this criterion:
[tex]\[
\mathbf{3.5 \times 10^3}
\][/tex]
Thus, the final answer is as follows:
For part (b): When you divide [tex]\(7 \times 10^5\)[/tex] by [tex]\(2 \times 10^2\)[/tex], the result is [tex]\(\mathbf{3.5 \times 10^3}\)[/tex].
The numerical value is: 3500.0
