If `(13^2-5^2)^(3//2)=6^3xxA`, then the value of A is:

Options

A. `2^3`
B. `2^4`
C. 2
D. `2^2`

Answer

To solve the equation \((13^2 - 5^2)^{3/2} = 6^3 \times A\), we will follow these steps:

### Step 1: Calculate \(13^2\) and \(5^2\)
First, we need to find the squares of 13 and 5:
\[ 13^2 = 169 \]
\[ 5^2 = 25 \]

### Step 2: Subtract \(5^2\) from \(13^2\)
Now, we subtract \(5^2\) from \(13^2\):
\[ 13^2 - 5^2 = 169 - 25 = 144 \]

### Step 3: Raise the result to the power of \(3/2\)
Next, we raise the result to the power of \(3/2\):
\[ (144)^{3/2} \]
This can be simplified as:
\[ (144^{1/2})^3 = (12)^3 = 1728 \]

### Step 4: Set the equation
Now we set up the equation:
\[ 1728 = 6^3 \times A \]

### Step 5: Calculate \(6^3\)
Next, we calculate \(6^3\):
\[ 6^3 = 216 \]

### Step 6: Substitute \(6^3\) back into the equation
Substituting \(6^3\) into the equation gives us:
\[ 1728 = 216 \times A \]

### Step 7: Solve for \(A\)
To find \(A\), we divide both sides by 216:
\[ A = \frac{1728}{216} \]
Calculating the division:
\[ A = 8 \]

### Conclusion
Thus, the value of \(A\) is:
\[ \boxed{8} \]