Simplify or otherwise reduce the following expression using the rules of exponents.
`8^(4)(5^(4))`

Answer

To simplify the expression \( 8^4 \times 5^4 \) using the rules of exponents, we can follow these steps:

### Step 1: Identify the bases and powers
The expression consists of two parts: \( 8^4 \) and \( 5^4 \). Both terms have the same exponent, which is 4.

### Step 2: Apply the law of exponents
According to the laws of exponents, when you multiply two expressions with the same exponent, you can combine the bases and keep the exponent. This is expressed as:
\[ a^m \times b^m = (a \times b)^m \]
In our case, we have:
\[ 8^4 \times 5^4 = (8 \times 5)^4 \]

### Step 3: Calculate the product of the bases
Now, we need to multiply the bases:
\[ 8 \times 5 = 40 \]

### Step 4: Write the final expression
Now we can substitute back into our expression:
\[ (8 \times 5)^4 = 40^4 \]

### Final Answer
Thus, the simplified expression is:
\[ 40^4 \]

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