4^0•5^-2/(-2)^-3

To simplify the given expression:

First, we will work with the exponents. Recall that for any nonzero number a, a^0 = 1.

So, 4^0 becomes 1.

Next, we'll apply the negative exponent rule, which states that a^-n = 1/a^n.

Therefore, 5^-2 becomes 1/5^2 = 1/25.

Finally, we'll simplify the expression by substituting the simplified values:

4^0 • 5^-2 / (-2)^-3 = 1 • 1/25 / (-1/8)

Recall that dividing by a fraction is equivalent to multiplying by its reciprocal:

= 1 • 1/25 • -8/-1

= 1/25 • 8/1

= 8/25