Solve (6×5)^(-8))^(-4): Compound Negative Exponents Problem

Insert the corresponding expression:

$\left(\left(6\times5\right)^{-8}\right)^{-4}=$

To solve this problem, we will follow these steps:

• Step 1: Apply the power of a power rule.

• Step 2: Simplify the resulting power.

Let's work through the process:

Step 1: Apply the power of a power rule, which states that $\left(a^m\right)^n = a^{m \times n}$.
We have $\left(\left(6\times5\right)^{-8}\right)^{-4}$. We can rewrite this using the power of a power rule:

$\left(\left(6\times5\right)^{-8}\right)^{-4} = \left(6\times5\right)^{-8 \times (-4)} = \left(6\times5\right)^{32}$

Step 2: By calculating the exponent: $-8 \times (-4) = 32$, we find the final simplified expression to be $\left(6\times5\right)^{32}$.

Therefore, the expression reduces to $\left(6\times5\right)^{32}$, which matches choice 2.