Sure, let's simplify the given expression step-by-step.
The initial expression we need to simplify is:
[tex]\[
\frac{1253^2 \times 84^1}{643^1 \times 83^2}
\][/tex]
### Step 1: Calculate the numerator \(1253^2 \times 84\)
- First, calculate \(1253^2\):
[tex]\[
1253^2 = 1253 \times 1253 = 1,570,009
\][/tex]
- Next, multiply this result by 84:
[tex]\[
1570009 \times 84 = 131,880,756
\][/tex]
So, the numerator is 131,880,756.
### Step 2: Calculate the denominator \(643 \times 83^2\)
- First, calculate \(83^2\):
[tex]\[
83^2 = 83 \times 83 = 6,889
\][/tex]
- Next, multiply this result by 643:
[tex]\[
643 \times 6889 = 4,429,627
\][/tex]
So, the denominator is 4,429,627.
### Step 3: Divide the numerator by the denominator
Now, divide the numerator (131,880,756) by the denominator (4,429,627) to get the simplified result:
[tex]\[
\frac{131880756}{4429627} \approx 29.772429145840047
\][/tex]
### Final Answer
So, the simplified value of the expression \(\frac{1253^2 \times 84}{643 \times 83^2}\) is approximately:
[tex]\[
29.772429145840047
\][/tex]
Therefore:
- The numerator is \(131,880,756\)
- The denominator is \(4,429,627\)
- The result is approximately [tex]\(29.772429145840047\)[/tex]
