Sure, let's solve the problem step-by-step.
### Step 1: Understanding the Problem
We are asked to calculate the value of 165 raised to the power of 0.382. Let's denote this as:
[tex]\[ 165^{0.382} \][/tex]
### Step 2: Calculate the Exact Value
First, we need to evaluate the expression \( 165^{0.382} \) precisely. The exact value of this expression is:
[tex]\[ 165^{0.382} = 7.032000074870731 \][/tex]
### Step 3: Round to Two Decimal Places
We need to round the exact value to two decimal places. The procedure for rounding is:
- Identify the digit in the second decimal place. Here, it is 3 in 7.032000074870731.
- Look at the digit immediately right of the second decimal place. Here, it is 2.
- Since the digit to the right (2) is less than 5, we do not round up the second decimal place.
Therefore, the value rounded to two decimal places is:
[tex]\[ 7.03 \][/tex]
### Final Answer
- The exact value of \( 165^{0.382} \) is: \( 7.032000074870731 \)
- Rounded to two decimal places, the value is: [tex]\( 7.03 \)[/tex]
