Calculate (13×4)^6: Evaluating a Power of Products Expression

The given expression to solve is $\left(13\times4\right)^6$. This expression involves raising a product to a power. According to the exponent rule, which is the Power of a Product Rule, the property can be stated as follows:

• When you have a product raised to an exponent, you can distribute the exponent to each factor in the product separately.

Mathematically, for any numbers $a$ and $b$, and a positive integer $n$, it is written as: $(a \times b)^n = a^n \times b^n$.

Applying this rule to our expression:

$\left(13 \times 4\right)^6$ becomes $13^6 \times 4^6$.

Thus, the expression $\left(13 \times 4\right)^6$ simplifies to $13^6 \times 4^6$ following the Power of a Product Rule.