Solve (4×5)^(-2): Evaluating Negative Exponents Step-by-Step

Insert the corresponding expression:

$\left(4\times5\right)^{-2}=$

To solve the problem, we must correctly apply the rules for exponents to distribute the given negative exponent across the factors in the expression:

The expression given is $\left(4 \times 5\right)^{-2}$. First, we apply the power of a product rule:

$\left(4 \times 5\right)^{-2} = 4^{-2} \times 5^{-2}$

This rule allows us to distribute the negative exponent $-2$ to both factors in the product inside the parentheses. Each factor is affected by the exponent.

Now, let’s verify this against the choices provided:

• Choice 3: $4^{-2} \times 5^{-2}$ matches our solution with proper application of the power of a product rule.

Therefore, the correct and corresponding expression is $\boxed{4^{-2}\times5^{-2}}$.