What is the value of `13xx(49)^((3)/(2))` ?

Options

A. 4369
B. 4459
C. 4549
D. 4639

Answer

To find the value of \( 13 \times (49)^{\frac{3}{2}} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ 13 \times (49)^{\frac{3}{2}} \]

### Step 2: Apply the power of a power rule
Using the property of exponents, we can rewrite \( (49)^{\frac{3}{2}} \) as:
\[ (49)^{\frac{3}{2}} = (49^{\frac{1}{2}})^3 \]
This means we first take the square root of 49 and then raise it to the power of 3.

### Step 3: Calculate the square root of 49
The square root of 49 is:
\[ 49^{\frac{1}{2}} = 7 \]

### Step 4: Raise the result to the power of 3
Now we raise 7 to the power of 3:
\[ 7^3 = 7 \times 7 \times 7 = 343 \]

### Step 5: Multiply by 13
Now we multiply this result by 13:
\[ 13 \times 343 \]

### Step 6: Perform the multiplication
To calculate \( 13 \times 343 \):
- First, calculate \( 13 \times 3 = 39 \) (write down 9 and carry over 3)
- Next, calculate \( 13 \times 4 = 52 \), and add the carry over 3: \( 52 + 3 = 55 \) (write down 5 and carry over 5)
- Finally, calculate \( 13 \times 3 = 39 \), and add the carry over 5: \( 39 + 5 = 44 \)

Putting it all together, we get:
\[ 13 \times 343 = 4459 \]

### Final Answer
Thus, the value of \( 13 \times (49)^{\frac{3}{2}} \) is:
\[ \boxed{4459} \]