Simplify 1/((2×7×8)^9): Complex Fraction with Power Expression

To solve this expression, we apply the rule for negative exponents.

The expression given is $\frac{1}{(2 \times 7 \times 8)^9}$. We recognize this as the reciprocal of a power, which can be rewritten using the negative exponent rule:

$\frac{1}{a^b} = a^{-b}$

Thus, $\frac{1}{(2 \times 7 \times 8)^9}$ can be rewritten as $(2 \times 7 \times 8)^{-9}$.

Thus, the correct answer is choice 1: $(2 \times 7 \times 8)^{-9}$.