Find value of `(61^(2)-11^(2))^(3/2)`.

Options

A. `50^(3)`
B. `216000`
C. 3600
D. 60

Explanation

To find the value of \((61^2 - 11^2)^{3/2}\), we can follow these steps:

### Step 1: Use the Difference of Squares Formula
The expression \(61^2 - 11^2\) can be simplified using the difference of squares formula:
\[ a^2 - b^2 = (a + b)(a - b) \]
Here, \(a = 61\) and \(b = 11\).

### Step 2: Calculate \(61 + 11\) and \(61 - 11\)
Now, let's calculate:
\[ 61 + 11 = 72 \]
\[ 61 - 11 = 50 \]

### Step 3: Substitute Back into the Formula
Now substitute these values back into the difference of squares formula:
\[ 61^2 - 11^2 = (61 + 11)(61 - 11) = 72 \times 50 \]

### Step 4: Calculate \(72 \times 50\)
Now calculate:
\[ 72 \times 50 = 3600 \]

### Step 5: Raise to the Power of \(\frac{3}{2}\)
Now we need to compute:
\[ (3600)^{3/2} \]

### Step 6: Calculate \((3600)^{3/2}\)
First, find the square root of 3600:
\[ \sqrt{3600} = 60 \]
Now raise it to the power of 3:
\[ 60^3 = 60 \times 60 \times 60 = 216000 \]

### Final Answer
Thus, the value of \((61^2 - 11^2)^{3/2}\) is:
\[ \boxed{216000} \]