Solve (12×7×9)^(-5): Negative Exponent Calculation

Start with $\left(12 \times 7 \times 9\right)^{-5}$.

Apply the power of a product property, which states $(xyz)^n = x^n \times y^n \times z^n$:
$\left(12 \times 7 \times 9\right)^{-5} = 12^{-5} \times 7^{-5} \times 9^{-5}$

Use the negative exponent property, $a^{-n} = \frac{1}{a^n}$:
$12^{-5} \times 7^{-5} \times 9^{-5} = \frac{1}{12^{5}} \times \frac{1}{7^{5}} \times \frac{1}{9^{5}}$

This results in:
$\frac{1}{12^5 \times 7^5 \times 9^5}$

Thus, the solution to the expression is $\frac{1}{12^5 \times 7^5 \times 9^5}$.

Keep in mind - we could have used the rules in the other way around, first the negative exponent rule, and only then the product rule and the result would still be the same!