Solve 4^x × 4^x: Product Rule of Exponential Expressions

To solve this problem, we will follow these steps:

• Step 1: Identify the given expression and the operation.

• Step 2: Apply the rule for multiplying powers with the same base.

• Step 3: Simplify the expression to reach the final answer.

Let's proceed with the solution:
Step 1: We are given the expression $4^x \times 4^x$. Both terms have the same base of 4 and an exponent of $x$.

Step 2: According to the exponent multiplication rule, $a^m \times a^n = a^{m+n}$. Here, since both bases are 4, we can simplify using this rule.

Step 3: We add the exponents, giving us:

$4^x \times 4^x = 4^{x+x} = 4^{2x}$

Therefore, the correct solution to the problem is $4^{x+x}$.