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

The expression in question is $\left(13\times4\right)^6$. This expression involves raising a product to a power and requires the application of the power of a product exponent rule, which states:

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

Mathematically, any numbers $a$ and $b$ and a positive integer $n$ can be written as$(a \times b)^n = a^n \times b^n$.

Applying this rule to our expression, $\left(13 \times 4\right)^6$ becomes $13^6 \times 4^6$.

Therefore, the expression $\left(13 \times 4\right)^6$ simplifies to $13^6 \times 4^6$.