Evaluate : `3^(4)xx5^(4)`

Answer

To evaluate the expression \( 3^4 \times 5^4 \), we can follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ 3^4 \times 5^4 \]

### Step 2: Apply the property of exponents
Since both terms have the same exponent (which is 4), we can use the property of exponents that states:
\[ a^m \times b^m = (a \times b)^m \]
In our case, \( a = 3 \), \( b = 5 \), and \( m = 4 \). Therefore, we can rewrite the expression as:
\[ (3 \times 5)^4 \]

### Step 3: Calculate the base
Now, we calculate the base:
\[ 3 \times 5 = 15 \]
So, we can rewrite the expression as:
\[ 15^4 \]

### Step 4: Evaluate \( 15^4 \)
Next, we need to calculate \( 15^4 \). This means multiplying 15 by itself four times:
\[ 15^4 = 15 \times 15 \times 15 \times 15 \]

### Step 5: Calculate \( 15^2 \)
First, we can calculate \( 15^2 \):
\[ 15 \times 15 = 225 \]

### Step 6: Calculate \( 15^4 \) using \( 15^2 \)
Now, we can use \( 15^2 \) to find \( 15^4 \):
\[ 15^4 = (15^2) \times (15^2) = 225 \times 225 \]

### Step 7: Calculate \( 225 \times 225 \)
Now we calculate \( 225 \times 225 \):
\[ 225 \times 225 = 50625 \]

### Final Answer
Thus, the value of \( 3^4 \times 5^4 \) is:
\[ \boxed{50625} \]