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

Choose the expression that corresponds to the following:

$\left(2\times9\times6\right)^{-7}=$

We first 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 get:
$\left(2\times9\times6\right)^{-7} = \frac{1}{\left(2\times9\times6\right)^7}$.

Therefore the correct answer is:
$\frac{1}{\left(2\times9\times6\right)^7}$

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