Compare `3xx2,3^(2)` and `2^(3)`

Options

A. ` 3^(2)` < `2^(3)` < `3xx2`
B. ` 3^(2)` < `2^(3)` > `3xx2`
C. ` 3^(2)` > `2^(3)` > `3xx2`
D. None of the above

Answer

To compare the expressions \(3 \times 2\), \(3^2\), and \(2^3\), we will evaluate each expression step by step.

### Step 1: Evaluate \(3 \times 2\)
\[ 3 \times 2 = 6 \]

### Step 2: Evaluate \(3^2\)
\[ 3^2 = 3 \times 3 = 9 \]

### Step 3: Evaluate \(2^3\)
\[ 2^3 = 2 \times 2 \times 2 = 4 \times 2 = 8 \]

### Step 4: Compare the results
Now we have the values:
- \(3 \times 2 = 6\)
- \(3^2 = 9\)
- \(2^3 = 8\)

### Step 5: Arrange the values in order
From the evaluations:
- \(3^2 = 9\) (the largest)
- \(2^3 = 8\) (the second largest)
- \(3 \times 2 = 6\) (the smallest)

Thus, we can conclude:
\[ 3^2 > 2^3 > 3 \times 2 \]

### Final Comparison Statement
So, the final comparison is:
\[ 3^2 > 2^3 > 3 \times 2 \]

---