Solve (9×7×8)^(-8): Negative Exponent Expression

To solve the expression $\left(9\times7\times8\right)^{-8}$, we need to apply the power of a product rule combined with the rule for negative exponents. The rule states that $a^{-n} = \frac{1}{a^n}$. So, a negative exponent indicates a reciprocal.

According to the power of a product rule, if you have a product raised to a power, it is the same as each factor being raised to that power: $(a \times b)^n = a^n \times b^n$.

So, applying the negative exponent rule to the original expression:

• Given: $\left(9\times7\times8\right)^{-8}$.

• Convert the negative exponent to positive by taking the reciprocal: $\frac{1}{\left(9\times7\times8\right)^8}$.

The correct expression after applying these rules is:

$\frac{1}{(9\times7\times8)^8}$.