Evaluate (2×9×6)^(-7): Negative Exponent of a Product

Let's solve the expression given as: $\left(2\times9\times6\right)^{-7}$.

We need to apply the exponent rule for powers with negative exponents, specifically the rule for the power of a product, which states that:
$\left(a \times b \times c \right)^{-n} = \frac{1}{(a \times b \times c)^n}$.

In this problem, we have three numbers multiplied inside the parentheses: 2, 9, and 6. The exponent is -7.

By applying the power of a product rule with a negative exponent here, we have:
$\left(2\times9\times6\right)^{-7} = \frac{1}{\left(2\times9\times6\right)^7}$.

This confirms the given correct answer:
$\frac{1}{\left(2\times9\times6\right)^7}$