Simplify the Expression: 4^6 Divided by (a^6 × x^6)

To solve this problem, we'll follow these steps:

• Step 1: Recognize the given expression $\frac{4^6}{a^6 \times x^6}$ is a power over a product raised to that power.
• Step 2: Apply the power of a quotient rule to rewrite the expression.

Now, let's work through each step:
Step 1: The given expression is $\frac{4^6}{a^6 \times x^6}$. This can be seen as having common exponents across the numerator and the denominator.
Step 2: Using the power of a quotient rule, which allows us to express the initial expression as $\left(\frac{4}{a \times x}\right)^6$. This step involves recognizing that you can treat the entire $a \times x$ as a single base for the denominator.

Hence, the simplified form of the given expression is $\left(\frac{4}{a \times x}\right)^6$.

Therefore, the solution to the problem is $\left(\frac{4}{a \times x}\right)^6$.