Evaluate ((7×4)^-6)^5: Complex Exponent Expression

To simplify the expression $\left(\left(7\times4\right)^{-6}\right)^5$, follow these steps, checking against the choices provided:

Step 1: Apply the power of a power rule.

• The expression inside the parentheses $7\times4$ acts as a single term $a$.

• Therefore, by applying $(a^m)^n = a^{m \times n}$, we simplify:

$\left(\left(7\times4\right)^{-6}\right)^5 = \left(7\times4\right)^{-6 \times 5}$

Step 2: Multiply the exponents.

• Calculate $-6 \times 5 = -30$.

• Hence, the expression simplifies to $\left(7\times4\right)^{-30}$.

Conclusion:

The correct simplified form of the expression is $\left(7\times4\right)^{-6\times5}$, aligning with choice 2 and your provided correct answer.